← Find the per-unit-weight rate first · Multiplicative Comparison and Unit Rate

Find the per-unit-weight rate first · 12 practice problems

3.OA.A.33.MD.A.2

Generated variants — 12

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 easy answer: $23

At the produce stand, Mia's mom buys 4 lb4\ \text{lb} of cherry tomatoes that cost $2\$2 per 8 oz8\ \text{oz}. At the butcher, she buys 1 lb1\ \text{lb} of pork that costs $7\$7 per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Show solution
1 · Understandwhat's really being asked

Mia's mom buys cherry tomatoes priced at $2 for every 8 oz and pork priced at $7 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens
  • Cherry tomatoes: she buys 4 lb (= 64 oz), priced at $2 per 8 oz.
  • Pork: she buys 1 lb, priced at $7 per pound.
  • 1 lb = 16 oz.
Unknowns
  • The total amount of money spent on the cherry tomatoes and the pork together.
Constraints
  • Prices are unit rates: $2 per 8 oz of tomatoes; $7 per 1 lb of pork.
  • Money amounts are in dollars and cents.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

This is a money/rate problem, so tracking the units ($ per ounce, $ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

3 · Execute3 carry out the plan

1Cost of the cherry tomatoes

#8 Analyze the Units 3.MD.A.2
4 lb is 64 oz, and the price is $2 for each 8 oz. There are 64 / 8 = 8 portions of 8 oz, so the tomatoes cost 8 groups of $2.
64÷8=8,8×$2=$1664 \div 8 = 8,\quad 8 \times \$2 = \$16
Converting 4 lb to 64 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

2Cost of the pork

#7 Identify Subproblems 3.OA.A.3
1 lb is 1 whole pound. At $7 per pound, the pork costs 1 x $7 = $7.
1×$7=$71 \times \$7 = \$7
Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

3Add the two costs

#7 Identify Subproblems 3.OA.A.3
Add the tomato cost and the pork cost to get the total spent.
$16+$7=$23\$16 + \$7 = \$23
Combining the two subtotals is a single addition of two money amounts.
Answer: $23
4 · Reviewdoes it hold up?

Tomatoes $16 and pork $7 are both sensible store prices, and the total $23 is a reasonable grocery sum for the two items.

Another way: Use repeated addition to confirm each subtotal, then add $16 + $7 to reach $23.

Standardsmin grade 3
  • 3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
  • 3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.
💡Takeaway. Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!
Variant 2 easy answer: $26

At the produce stand, Mia's mom buys 2 lb2\ \text{lb} of cherry tomatoes that cost $3\$3 per 8 oz8\ \text{oz}. At the butcher, she buys 2 lb2\ \text{lb} of pork that costs $7\$7 per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Show solution
1 · Understandwhat's really being asked

Mia's mom buys cherry tomatoes priced at $3 for every 8 oz and pork priced at $7 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens
  • Cherry tomatoes: she buys 2 lb (= 32 oz), priced at $3 per 8 oz.
  • Pork: she buys 2 lb, priced at $7 per pound.
  • 1 lb = 16 oz.
Unknowns
  • The total amount of money spent on the cherry tomatoes and the pork together.
Constraints
  • Prices are unit rates: $3 per 8 oz of tomatoes; $7 per 1 lb of pork.
  • Money amounts are in dollars and cents.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

This is a money/rate problem, so tracking the units ($ per ounce, $ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

3 · Execute3 carry out the plan

1Cost of the cherry tomatoes

#8 Analyze the Units 3.MD.A.2
2 lb is 32 oz, and the price is $3 for each 8 oz. There are 32 / 8 = 4 portions of 8 oz, so the tomatoes cost 4 groups of $3.
32÷8=4,4×$3=$1232 \div 8 = 4,\quad 4 \times \$3 = \$12
Converting 2 lb to 32 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

2Cost of the pork

#7 Identify Subproblems 3.OA.A.3
2 lb is 2 whole pounds. At $7 per pound, the pork costs 2 x $7 = $14.
2×$7=$142 \times \$7 = \$14
Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

3Add the two costs

#7 Identify Subproblems 3.OA.A.3
Add the tomato cost and the pork cost to get the total spent.
$12+$14=$26\$12 + \$14 = \$26
Combining the two subtotals is a single addition of two money amounts.
Answer: $26
4 · Reviewdoes it hold up?

Tomatoes $12 and pork $14 are both sensible store prices, and the total $26 is a reasonable grocery sum for the two items.

Another way: Use repeated addition to confirm each subtotal, then add $12 + $14 to reach $26.

Standardsmin grade 3
  • 3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
  • 3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.
💡Takeaway. Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!
Variant 3 easy answer: $19

At the produce stand, Mia's mom buys 1 lb1\ \text{lb} of cherry tomatoes that cost $7\$7 per 8 oz8\ \text{oz}. At the butcher, she buys 1 lb1\ \text{lb} of pork that costs $5\$5 per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Show solution
1 · Understandwhat's really being asked

Mia's mom buys cherry tomatoes priced at $7 for every 8 oz and pork priced at $5 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens
  • Cherry tomatoes: she buys 1 lb (= 16 oz), priced at $7 per 8 oz.
  • Pork: she buys 1 lb, priced at $5 per pound.
  • 1 lb = 16 oz.
Unknowns
  • The total amount of money spent on the cherry tomatoes and the pork together.
Constraints
  • Prices are unit rates: $7 per 8 oz of tomatoes; $5 per 1 lb of pork.
  • Money amounts are in dollars and cents.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

This is a money/rate problem, so tracking the units ($ per ounce, $ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

3 · Execute3 carry out the plan

1Cost of the cherry tomatoes

#8 Analyze the Units 3.MD.A.2
1 lb is 16 oz, and the price is $7 for each 8 oz. There are 16 / 8 = 2 portions of 8 oz, so the tomatoes cost 2 groups of $7.
16÷8=2,2×$7=$1416 \div 8 = 2,\quad 2 \times \$7 = \$14
Converting 1 lb to 16 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

2Cost of the pork

#7 Identify Subproblems 3.OA.A.3
1 lb is 1 whole pound. At $5 per pound, the pork costs 1 x $5 = $5.
1×$5=$51 \times \$5 = \$5
Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

3Add the two costs

#7 Identify Subproblems 3.OA.A.3
Add the tomato cost and the pork cost to get the total spent.
$14+$5=$19\$14 + \$5 = \$19
Combining the two subtotals is a single addition of two money amounts.
Answer: $19
4 · Reviewdoes it hold up?

Tomatoes $14 and pork $5 are both sensible store prices, and the total $19 is a reasonable grocery sum for the two items.

Another way: Use repeated addition to confirm each subtotal, then add $14 + $5 to reach $19.

Standardsmin grade 3
  • 3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
  • 3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.
💡Takeaway. Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!
Variant 4 easy answer: $38

At the produce stand, Mia's mom buys 2 lb2\ \text{lb} of cherry tomatoes that cost $5\$5 per 8 oz8\ \text{oz}. At the butcher, she buys 2 lb2\ \text{lb} of pork that costs $9\$9 per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Show solution
1 · Understandwhat's really being asked

Mia's mom buys cherry tomatoes priced at $5 for every 8 oz and pork priced at $9 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens
  • Cherry tomatoes: she buys 2 lb (= 32 oz), priced at $5 per 8 oz.
  • Pork: she buys 2 lb, priced at $9 per pound.
  • 1 lb = 16 oz.
Unknowns
  • The total amount of money spent on the cherry tomatoes and the pork together.
Constraints
  • Prices are unit rates: $5 per 8 oz of tomatoes; $9 per 1 lb of pork.
  • Money amounts are in dollars and cents.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

This is a money/rate problem, so tracking the units ($ per ounce, $ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

3 · Execute3 carry out the plan

1Cost of the cherry tomatoes

#8 Analyze the Units 3.MD.A.2
2 lb is 32 oz, and the price is $5 for each 8 oz. There are 32 / 8 = 4 portions of 8 oz, so the tomatoes cost 4 groups of $5.
32÷8=4,4×$5=$2032 \div 8 = 4,\quad 4 \times \$5 = \$20
Converting 2 lb to 32 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

2Cost of the pork

#7 Identify Subproblems 3.OA.A.3
2 lb is 2 whole pounds. At $9 per pound, the pork costs 2 x $9 = $18.
2×$9=$182 \times \$9 = \$18
Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

3Add the two costs

#7 Identify Subproblems 3.OA.A.3
Add the tomato cost and the pork cost to get the total spent.
$20+$18=$38\$20 + \$18 = \$38
Combining the two subtotals is a single addition of two money amounts.
Answer: $38
4 · Reviewdoes it hold up?

Tomatoes $20 and pork $18 are both sensible store prices, and the total $38 is a reasonable grocery sum for the two items.

Another way: Use repeated addition to confirm each subtotal, then add $20 + $18 to reach $38.

Standardsmin grade 3
  • 3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
  • 3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.
💡Takeaway. Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!
Variant 5 medium answer: $22

At the produce stand, Mia's mom buys 3 lb3\ \text{lb} of cherry tomatoes that cost $2\$2 per 8 oz8\ \text{oz}. At the butcher, she buys 1 lb1\ \text{lb} of pork that costs $10\$10 per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Show solution
1 · Understandwhat's really being asked

Mia's mom buys cherry tomatoes priced at $2 for every 8 oz and pork priced at $10 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens
  • Cherry tomatoes: she buys 3 lb (= 48 oz), priced at $2 per 8 oz.
  • Pork: she buys 1 lb, priced at $10 per pound.
  • 1 lb = 16 oz.
Unknowns
  • The total amount of money spent on the cherry tomatoes and the pork together.
Constraints
  • Prices are unit rates: $2 per 8 oz of tomatoes; $10 per 1 lb of pork.
  • Money amounts are in dollars and cents.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

This is a money/rate problem, so tracking the units ($ per ounce, $ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

3 · Execute3 carry out the plan

1Cost of the cherry tomatoes

#8 Analyze the Units 3.MD.A.2
3 lb is 48 oz, and the price is $2 for each 8 oz. There are 48 / 8 = 6 portions of 8 oz, so the tomatoes cost 6 groups of $2.
48÷8=6,6×$2=$1248 \div 8 = 6,\quad 6 \times \$2 = \$12
Converting 3 lb to 48 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

2Cost of the pork

#7 Identify Subproblems 3.OA.A.3
1 lb is 1 whole pound. At $10 per pound, the pork costs 1 x $10 = $10.
1×$10=$101 \times \$10 = \$10
Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

3Add the two costs

#7 Identify Subproblems 3.OA.A.3
Add the tomato cost and the pork cost to get the total spent.
$12+$10=$22\$12 + \$10 = \$22
Combining the two subtotals is a single addition of two money amounts.
Answer: $22
4 · Reviewdoes it hold up?

Tomatoes $12 and pork $10 are both sensible store prices, and the total $22 is a reasonable grocery sum for the two items.

Another way: Use repeated addition to confirm each subtotal, then add $12 + $10 to reach $22.

Standardsmin grade 3
  • 3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
  • 3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.
💡Takeaway. Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!
Variant 6 medium answer: $42

At the produce stand, Mia's mom buys 1 lb1\ \text{lb} of cherry tomatoes that cost $9\$9 per 8 oz8\ \text{oz}. At the butcher, she buys 2 lb2\ \text{lb} of pork that costs $12\$12 per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Show solution
1 · Understandwhat's really being asked

Mia's mom buys cherry tomatoes priced at $9 for every 8 oz and pork priced at $12 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens
  • Cherry tomatoes: she buys 1 lb (= 16 oz), priced at $9 per 8 oz.
  • Pork: she buys 2 lb, priced at $12 per pound.
  • 1 lb = 16 oz.
Unknowns
  • The total amount of money spent on the cherry tomatoes and the pork together.
Constraints
  • Prices are unit rates: $9 per 8 oz of tomatoes; $12 per 1 lb of pork.
  • Money amounts are in dollars and cents.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

This is a money/rate problem, so tracking the units ($ per ounce, $ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

3 · Execute3 carry out the plan

1Cost of the cherry tomatoes

#8 Analyze the Units 3.MD.A.2
1 lb is 16 oz, and the price is $9 for each 8 oz. There are 16 / 8 = 2 portions of 8 oz, so the tomatoes cost 2 groups of $9.
16÷8=2,2×$9=$1816 \div 8 = 2,\quad 2 \times \$9 = \$18
Converting 1 lb to 16 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

2Cost of the pork

#7 Identify Subproblems 3.OA.A.3
2 lb is 2 whole pounds. At $12 per pound, the pork costs 2 x $12 = $24.
2×$12=$242 \times \$12 = \$24
Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

3Add the two costs

#7 Identify Subproblems 3.OA.A.3
Add the tomato cost and the pork cost to get the total spent.
$18+$24=$42\$18 + \$24 = \$42
Combining the two subtotals is a single addition of two money amounts.
Answer: $42
4 · Reviewdoes it hold up?

Tomatoes $18 and pork $24 are both sensible store prices, and the total $42 is a reasonable grocery sum for the two items.

Another way: Use repeated addition to confirm each subtotal, then add $18 + $24 to reach $42.

Standardsmin grade 3
  • 3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
  • 3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.
💡Takeaway. Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!
Variant 7 medium answer: $44

At the produce stand, Mia's mom buys 2 lb2\ \text{lb} of cherry tomatoes that cost $6\$6 per 8 oz8\ \text{oz}. At the butcher, she buys 2 lb 8 oz2\ \text{lb}\ 8\ \text{oz} of pork that costs $8\$8 per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Show solution
1 · Understandwhat's really being asked

Mia's mom buys cherry tomatoes priced at $6 for every 8 oz and pork priced at $8 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens
  • Cherry tomatoes: she buys 2 lb (= 32 oz), priced at $6 per 8 oz.
  • Pork: she buys 2 lb 8 oz, priced at $8 per pound.
  • 1 lb = 16 oz.
Unknowns
  • The total amount of money spent on the cherry tomatoes and the pork together.
Constraints
  • Prices are unit rates: $6 per 8 oz of tomatoes; $8 per 1 lb of pork.
  • Money amounts are in dollars and cents.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

This is a money/rate problem, so tracking the units ($ per ounce, $ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

3 · Execute3 carry out the plan

1Cost of the cherry tomatoes

#8 Analyze the Units 3.MD.A.2
2 lb is 32 oz, and the price is $6 for each 8 oz. There are 32 / 8 = 4 portions of 8 oz, so the tomatoes cost 4 groups of $6.
32÷8=4,4×$6=$2432 \div 8 = 4,\quad 4 \times \$6 = \$24
Converting 2 lb to 32 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

2Cost of the pork

#7 Identify Subproblems 3.OA.A.3
2 lb 8 oz is 2 whole pounds plus half a pound (8 oz = half of 16 oz). At $8 per pound, 2 pounds cost $16 and the extra half-pound costs half of $8, which is $4.
2×$8+12×$8=$16+$4=$202\times\$8 + \tfrac{1}{2}\times\$8 = \$16 + \$4 = \$20
Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

3Add the two costs

#7 Identify Subproblems 3.OA.A.3
Add the tomato cost and the pork cost to get the total spent.
$24+$20=$44\$24 + \$20 = \$44
Combining the two subtotals is a single addition of two money amounts.
Answer: $44
4 · Reviewdoes it hold up?

Tomatoes $24 and pork $20 are both sensible store prices, and the total $44 is a reasonable grocery sum for the two items.

Another way: Use repeated addition to confirm each subtotal, then add $24 + $20 to reach $44.

Standardsmin grade 3
  • 3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
  • 3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.
💡Takeaway. Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!
Variant 8 hard answer: $30

At the produce stand, Mia's mom buys 3 lb3\ \text{lb} of cherry tomatoes that cost $3\$3 per 8 oz8\ \text{oz}. At the butcher, she buys 1 lb 8 oz1\ \text{lb}\ 8\ \text{oz} of pork that costs $8\$8 per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Show solution
1 · Understandwhat's really being asked

Mia's mom buys cherry tomatoes priced at $3 for every 8 oz and pork priced at $8 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens
  • Cherry tomatoes: she buys 3 lb (= 48 oz), priced at $3 per 8 oz.
  • Pork: she buys 1 lb 8 oz, priced at $8 per pound.
  • 1 lb = 16 oz.
Unknowns
  • The total amount of money spent on the cherry tomatoes and the pork together.
Constraints
  • Prices are unit rates: $3 per 8 oz of tomatoes; $8 per 1 lb of pork.
  • Money amounts are in dollars and cents.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

This is a money/rate problem, so tracking the units ($ per ounce, $ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

3 · Execute3 carry out the plan

1Cost of the cherry tomatoes

#8 Analyze the Units 3.MD.A.2
3 lb is 48 oz, and the price is $3 for each 8 oz. There are 48 / 8 = 6 portions of 8 oz, so the tomatoes cost 6 groups of $3.
48÷8=6,6×$3=$1848 \div 8 = 6,\quad 6 \times \$3 = \$18
Converting 3 lb to 48 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

2Cost of the pork

#7 Identify Subproblems 3.OA.A.3
1 lb 8 oz is 1 whole pound plus half a pound (8 oz = half of 16 oz). At $8 per pound, 1 pound cost $8 and the extra half-pound costs half of $8, which is $4.
1×$8+12×$8=$8+$4=$121\times\$8 + \tfrac{1}{2}\times\$8 = \$8 + \$4 = \$12
Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

3Add the two costs

#7 Identify Subproblems 3.OA.A.3
Add the tomato cost and the pork cost to get the total spent.
$18+$12=$30\$18 + \$12 = \$30
Combining the two subtotals is a single addition of two money amounts.
Answer: $30
4 · Reviewdoes it hold up?

Tomatoes $18 and pork $12 are both sensible store prices, and the total $30 is a reasonable grocery sum for the two items.

Another way: Use repeated addition to confirm each subtotal, then add $18 + $12 to reach $30.

Standardsmin grade 3
  • 3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
  • 3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.
💡Takeaway. Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!
Variant 9 hard answer: $43

At the produce stand, Mia's mom buys 1 lb1\ \text{lb} of cherry tomatoes that cost $8\$8 per 8 oz8\ \text{oz}. At the butcher, she buys 4 lb 8 oz4\ \text{lb}\ 8\ \text{oz} of pork that costs $6\$6 per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Show solution
1 · Understandwhat's really being asked

Mia's mom buys cherry tomatoes priced at $8 for every 8 oz and pork priced at $6 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens
  • Cherry tomatoes: she buys 1 lb (= 16 oz), priced at $8 per 8 oz.
  • Pork: she buys 4 lb 8 oz, priced at $6 per pound.
  • 1 lb = 16 oz.
Unknowns
  • The total amount of money spent on the cherry tomatoes and the pork together.
Constraints
  • Prices are unit rates: $8 per 8 oz of tomatoes; $6 per 1 lb of pork.
  • Money amounts are in dollars and cents.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

This is a money/rate problem, so tracking the units ($ per ounce, $ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

3 · Execute3 carry out the plan

1Cost of the cherry tomatoes

#8 Analyze the Units 3.MD.A.2
1 lb is 16 oz, and the price is $8 for each 8 oz. There are 16 / 8 = 2 portions of 8 oz, so the tomatoes cost 2 groups of $8.
16÷8=2,2×$8=$1616 \div 8 = 2,\quad 2 \times \$8 = \$16
Converting 1 lb to 16 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

2Cost of the pork

#7 Identify Subproblems 3.OA.A.3
4 lb 8 oz is 4 whole pounds plus half a pound (8 oz = half of 16 oz). At $6 per pound, 4 pounds cost $24 and the extra half-pound costs half of $6, which is $3.
4×$6+12×$6=$24+$3=$274\times\$6 + \tfrac{1}{2}\times\$6 = \$24 + \$3 = \$27
Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

3Add the two costs

#7 Identify Subproblems 3.OA.A.3
Add the tomato cost and the pork cost to get the total spent.
$16+$27=$43\$16 + \$27 = \$43
Combining the two subtotals is a single addition of two money amounts.
Answer: $43
4 · Reviewdoes it hold up?

Tomatoes $16 and pork $27 are both sensible store prices, and the total $43 is a reasonable grocery sum for the two items.

Another way: Use repeated addition to confirm each subtotal, then add $16 + $27 to reach $43.

Standardsmin grade 3
  • 3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
  • 3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.
💡Takeaway. Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!
Variant 10 hard answer: $30

At the produce stand, Mia's mom buys 2 lb2\ \text{lb} of cherry tomatoes that cost $4\$4 per 8 oz8\ \text{oz}. At the butcher, she buys 3 lb 8 oz3\ \text{lb}\ 8\ \text{oz} of pork that costs $4\$4 per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Show solution
1 · Understandwhat's really being asked

Mia's mom buys cherry tomatoes priced at $4 for every 8 oz and pork priced at $4 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens
  • Cherry tomatoes: she buys 2 lb (= 32 oz), priced at $4 per 8 oz.
  • Pork: she buys 3 lb 8 oz, priced at $4 per pound.
  • 1 lb = 16 oz.
Unknowns
  • The total amount of money spent on the cherry tomatoes and the pork together.
Constraints
  • Prices are unit rates: $4 per 8 oz of tomatoes; $4 per 1 lb of pork.
  • Money amounts are in dollars and cents.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

This is a money/rate problem, so tracking the units ($ per ounce, $ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

3 · Execute3 carry out the plan

1Cost of the cherry tomatoes

#8 Analyze the Units 3.MD.A.2
2 lb is 32 oz, and the price is $4 for each 8 oz. There are 32 / 8 = 4 portions of 8 oz, so the tomatoes cost 4 groups of $4.
32÷8=4,4×$4=$1632 \div 8 = 4,\quad 4 \times \$4 = \$16
Converting 2 lb to 32 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

2Cost of the pork

#7 Identify Subproblems 3.OA.A.3
3 lb 8 oz is 3 whole pounds plus half a pound (8 oz = half of 16 oz). At $4 per pound, 3 pounds cost $12 and the extra half-pound costs half of $4, which is $2.
3×$4+12×$4=$12+$2=$143\times\$4 + \tfrac{1}{2}\times\$4 = \$12 + \$2 = \$14
Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

3Add the two costs

#7 Identify Subproblems 3.OA.A.3
Add the tomato cost and the pork cost to get the total spent.
$16+$14=$30\$16 + \$14 = \$30
Combining the two subtotals is a single addition of two money amounts.
Answer: $30
4 · Reviewdoes it hold up?

Tomatoes $16 and pork $14 are both sensible store prices, and the total $30 is a reasonable grocery sum for the two items.

Another way: Use repeated addition to confirm each subtotal, then add $16 + $14 to reach $30.

Standardsmin grade 3
  • 3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
  • 3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.
💡Takeaway. Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!
Variant 11 medium answer: $31

At the produce stand, Mia's mom buys 1 lb1\ \text{lb} of cherry tomatoes that cost $5\$5 per 8 oz8\ \text{oz}. At the butcher, she buys 3 lb 8 oz3\ \text{lb}\ 8\ \text{oz} of pork that costs $6\$6 per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Show solution
1 · Understandwhat's really being asked

Mia's mom buys cherry tomatoes priced at $5 for every 8 oz and pork priced at $6 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens
  • Cherry tomatoes: she buys 1 lb (= 16 oz), priced at $5 per 8 oz.
  • Pork: she buys 3 lb 8 oz, priced at $6 per pound.
  • 1 lb = 16 oz.
Unknowns
  • The total amount of money spent on the cherry tomatoes and the pork together.
Constraints
  • Prices are unit rates: $5 per 8 oz of tomatoes; $6 per 1 lb of pork.
  • Money amounts are in dollars and cents.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

This is a money/rate problem, so tracking the units ($ per ounce, $ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

3 · Execute3 carry out the plan

1Cost of the cherry tomatoes

#8 Analyze the Units 3.MD.A.2
1 lb is 16 oz, and the price is $5 for each 8 oz. There are 16 / 8 = 2 portions of 8 oz, so the tomatoes cost 2 groups of $5.
16÷8=2,2×$5=$1016 \div 8 = 2,\quad 2 \times \$5 = \$10
Converting 1 lb to 16 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

2Cost of the pork

#7 Identify Subproblems 3.OA.A.3
3 lb 8 oz is 3 whole pounds plus half a pound (8 oz = half of 16 oz). At $6 per pound, 3 pounds cost $18 and the extra half-pound costs half of $6, which is $3.
3×$6+12×$6=$18+$3=$213\times\$6 + \tfrac{1}{2}\times\$6 = \$18 + \$3 = \$21
Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

3Add the two costs

#7 Identify Subproblems 3.OA.A.3
Add the tomato cost and the pork cost to get the total spent.
$10+$21=$31\$10 + \$21 = \$31
Combining the two subtotals is a single addition of two money amounts.
Answer: $31
4 · Reviewdoes it hold up?

Tomatoes $10 and pork $21 are both sensible store prices, and the total $31 is a reasonable grocery sum for the two items.

Another way: Use repeated addition to confirm each subtotal, then add $10 + $21 to reach $31.

Standardsmin grade 3
  • 3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
  • 3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.
💡Takeaway. Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!
Variant 12 hard answer: $21.50

At the produce stand, Mia's mom buys 1 lb1\ \text{lb} of cherry tomatoes that cost $4\$4 per 8 oz8\ \text{oz}. At the butcher, she buys 1 lb 8 oz1\ \text{lb}\ 8\ \text{oz} of pork that costs $9\$9 per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Show solution
1 · Understandwhat's really being asked

Mia's mom buys cherry tomatoes priced at $4 for every 8 oz and pork priced at $9 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens
  • Cherry tomatoes: she buys 1 lb (= 16 oz), priced at $4 per 8 oz.
  • Pork: she buys 1 lb 8 oz, priced at $9 per pound.
  • 1 lb = 16 oz.
Unknowns
  • The total amount of money spent on the cherry tomatoes and the pork together.
Constraints
  • Prices are unit rates: $4 per 8 oz of tomatoes; $9 per 1 lb of pork.
  • Money amounts are in dollars and cents.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems

This is a money/rate problem, so tracking the units ($ per ounce, $ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

3 · Execute3 carry out the plan

1Cost of the cherry tomatoes

#8 Analyze the Units 3.MD.A.2
1 lb is 16 oz, and the price is $4 for each 8 oz. There are 16 / 8 = 2 portions of 8 oz, so the tomatoes cost 2 groups of $4.
16÷8=2,2×$4=$816 \div 8 = 2,\quad 2 \times \$4 = \$8
Converting 1 lb to 16 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

2Cost of the pork

#7 Identify Subproblems 3.OA.A.3
1 lb 8 oz is 1 whole pound plus half a pound (8 oz = half of 16 oz). At $9 per pound, 1 pound cost $9 and the extra half-pound costs half of $9, which is $4.50.
1×$9+12×$9=$9+$4.50=$13.501\times\$9 + \tfrac{1}{2}\times\$9 = \$9 + \$4.50 = \$13.50
Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

3Add the two costs

#7 Identify Subproblems 3.OA.A.3
Add the tomato cost and the pork cost to get the total spent.
$8+$13.50=$21.50\$8 + \$13.50 = \$21.50
Combining the two subtotals is a single addition of two money amounts.
Answer: $21.50
4 · Reviewdoes it hold up?

Tomatoes $8 and pork $13.50 are both sensible store prices, and the total $21.50 is a reasonable grocery sum for the two items.

Another way: Use repeated addition to confirm each subtotal, then add $8 + $13.50 to reach $21.50.

Standardsmin grade 3
  • 3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
  • 3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.
💡Takeaway. Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!