← Find the value of one unit · Multiplicative Comparison and Unit Rate

Find the value of one unit · 10 practice problems

4.NBT.B.64.OA.A.2

Generated variants — 10

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

Variant 1 easy answer: The craft store (at $0.65 per marble versus $0.75 at the supermarket).

A craft store sells $15$ marbles for $\$9.75$ , and a supermarket sells $12$ marbles for $\$9.00$ . Find which store sells the marbles more cheaply.

Show solution

1 · Understandwhat's really being asked

A craft store sells 15 marbles for $9.75 and a supermarket sells 12 marbles for $9.00. Find which store sells marbles more cheaply by comparing the price of a single marble.

Givens

Craft store: 15 marbles cost $9.75
Supermarket: 12 marbles cost $9.00
We want the cheaper store per marble

Unknowns

The price of one marble at each store, and which is lower

Constraints

Price per marble equals total price divided by the number of marbles
The cheaper store is the one with the smaller price per marble

2 · Planchoose the strategy

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

To compare bundles of different sizes fairly, reduce each to the same unit -- the price of one marble (dollars per marble) -- by dividing total price by count. The smaller per-marble price wins.

3 · Execute3 carry out the plan

1Price per marble at the craft store

#8 Analyze the Units 4.NBT.B.6

Divide the total by the number of marbles: $9.75 / 15 = $0.65 per marble.

9.75 \div 15 = 0.65

Splitting the total cost equally among 15 marbles gives the cost of just one.

2Price per marble at the supermarket

#8 Analyze the Units 4.NBT.B.6

Divide the total by the number of marbles: $9.00 / 12 = $0.75 per marble.

9.00 \div 12 = 0.75

The same one-unit idea applied to the supermarket bundle.

3Compare the unit prices

#7 Identify Subproblems 4.OA.A.2

Compare $0.65 and $0.75 per marble. Since $0.65 is less than $0.75, the craft store sells marbles more cheaply.

0.65 < 0.75

Once both are measured per single marble, the smaller number is the better deal.

Answer: The craft store (at $0.65 per marble versus $0.75 at the supermarket).

4 · Reviewdoes it hold up?

Cross-check with equal counts: 180 marbles cost 12 x $9.75 = $117.00 at the craft store but 15 x $9.00 = $135.00 at the supermarket, so the craft store is cheaper, agreeing with the per-marble result.

Another way: Identify subproblems (tool 7) by scaling to a common count: find the cost of 180 marbles at each store and compare $117.00 with $135.00 directly.

Standardsmin grade 4

4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison — Comparing the two stores by their per-marble unit prices.
4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing each total price by the number of marbles to get the unit price.

💡Takeaway. This only needs Grade 4 dividing -- find the price of one marble at each store, and the smaller one is the better deal!

Variant 2 easy answer: The supermarket (at $0.40 per marble versus $0.45 at the craft store).

A craft store sells $20$ marbles for $\$9.00$ , and a supermarket sells $15$ marbles for $\$6.00$ . Find which store sells the marbles more cheaply.

Show solution

1 · Understandwhat's really being asked

A craft store sells 20 marbles for $9.00 and a supermarket sells 15 marbles for $6.00. Find which store sells marbles more cheaply by comparing the price of a single marble.

Givens

Craft store: 20 marbles cost $9.00
Supermarket: 15 marbles cost $6.00
We want the cheaper store per marble

Unknowns

The price of one marble at each store, and which is lower

Constraints

Price per marble equals total price divided by the number of marbles
The cheaper store is the one with the smaller price per marble

2 · Planchoose the strategy

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

To compare bundles of different sizes fairly, reduce each to the same unit -- the price of one marble (dollars per marble) -- by dividing total price by count. The smaller per-marble price wins.

3 · Execute3 carry out the plan

1Price per marble at the craft store

#8 Analyze the Units 4.NBT.B.6

Divide the total by the number of marbles: $9.00 / 20 = $0.45 per marble.

9.00 \div 20 = 0.45

Splitting the total cost equally among 20 marbles gives the cost of just one.

2Price per marble at the supermarket

#8 Analyze the Units 4.NBT.B.6

Divide the total by the number of marbles: $6.00 / 15 = $0.40 per marble.

6.00 \div 15 = 0.40

The same one-unit idea applied to the supermarket bundle.

3Compare the unit prices

#7 Identify Subproblems 4.OA.A.2

Compare $0.45 and $0.40 per marble. Since $0.40 is less than $0.45, the supermarket sells marbles more cheaply.

0.45 > 0.40

Once both are measured per single marble, the smaller number is the better deal.

Answer: The supermarket (at $0.40 per marble versus $0.45 at the craft store).

4 · Reviewdoes it hold up?

Cross-check with equal counts: 300 marbles cost 15 x $9.00 = $135.00 at the craft store but 20 x $6.00 = $120.00 at the supermarket, so the supermarket is cheaper, agreeing with the per-marble result.

Another way: Identify subproblems (tool 7) by scaling to a common count: find the cost of 300 marbles at each store and compare $135.00 with $120.00 directly.

Standardsmin grade 4

4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison — Comparing the two stores by their per-marble unit prices.
4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing each total price by the number of marbles to get the unit price.

💡Takeaway. This only needs Grade 4 dividing -- find the price of one marble at each store, and the smaller one is the better deal!

Variant 3 easy answer: The craft store (at $0.25 per marble versus $0.30 at the supermarket).

A craft store sells $16$ marbles for $\$4.00$ , and a supermarket sells $20$ marbles for $\$6.00$ . Find which store sells the marbles more cheaply.

Show solution

1 · Understandwhat's really being asked

A craft store sells 16 marbles for $4.00 and a supermarket sells 20 marbles for $6.00. Find which store sells marbles more cheaply by comparing the price of a single marble.

Givens

Craft store: 16 marbles cost $4.00
Supermarket: 20 marbles cost $6.00
We want the cheaper store per marble

Unknowns

The price of one marble at each store, and which is lower

Constraints

Price per marble equals total price divided by the number of marbles
The cheaper store is the one with the smaller price per marble

2 · Planchoose the strategy

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

To compare bundles of different sizes fairly, reduce each to the same unit -- the price of one marble (dollars per marble) -- by dividing total price by count. The smaller per-marble price wins.

3 · Execute3 carry out the plan

1Price per marble at the craft store

#8 Analyze the Units 4.NBT.B.6

Divide the total by the number of marbles: $4.00 / 16 = $0.25 per marble.

4.00 \div 16 = 0.25

Splitting the total cost equally among 16 marbles gives the cost of just one.

2Price per marble at the supermarket

#8 Analyze the Units 4.NBT.B.6

Divide the total by the number of marbles: $6.00 / 20 = $0.30 per marble.

6.00 \div 20 = 0.30

The same one-unit idea applied to the supermarket bundle.

3Compare the unit prices

#7 Identify Subproblems 4.OA.A.2

Compare $0.25 and $0.30 per marble. Since $0.25 is less than $0.30, the craft store sells marbles more cheaply.

0.25 < 0.30

Once both are measured per single marble, the smaller number is the better deal.

Answer: The craft store (at $0.25 per marble versus $0.30 at the supermarket).

4 · Reviewdoes it hold up?

Cross-check with equal counts: 320 marbles cost 20 x $4.00 = $80.00 at the craft store but 16 x $6.00 = $96.00 at the supermarket, so the craft store is cheaper, agreeing with the per-marble result.

Another way: Identify subproblems (tool 7) by scaling to a common count: find the cost of 320 marbles at each store and compare $80.00 with $96.00 directly.

Standardsmin grade 4

4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison — Comparing the two stores by their per-marble unit prices.
4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing each total price by the number of marbles to get the unit price.

💡Takeaway. This only needs Grade 4 dividing -- find the price of one marble at each store, and the smaller one is the better deal!

Variant 4 medium answer: The supermarket (at $0.40 per marble versus $0.45 at the craft store).

A craft store sells $18$ marbles for $\$8.10$ , and a supermarket sells $22$ marbles for $\$8.80$ . Find which store sells the marbles more cheaply.

Show solution

1 · Understandwhat's really being asked

A craft store sells 18 marbles for $8.10 and a supermarket sells 22 marbles for $8.80. Find which store sells marbles more cheaply by comparing the price of a single marble.

Givens

Craft store: 18 marbles cost $8.10
Supermarket: 22 marbles cost $8.80
We want the cheaper store per marble

Unknowns

The price of one marble at each store, and which is lower

Constraints

Price per marble equals total price divided by the number of marbles
The cheaper store is the one with the smaller price per marble

2 · Planchoose the strategy

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

To compare bundles of different sizes fairly, reduce each to the same unit -- the price of one marble (dollars per marble) -- by dividing total price by count. The smaller per-marble price wins.

3 · Execute3 carry out the plan

1Price per marble at the craft store

#8 Analyze the Units 4.NBT.B.6

Divide the total by the number of marbles: $8.10 / 18 = $0.45 per marble.

8.10 \div 18 = 0.45

Splitting the total cost equally among 18 marbles gives the cost of just one.

2Price per marble at the supermarket

#8 Analyze the Units 4.NBT.B.6

Divide the total by the number of marbles: $8.80 / 22 = $0.40 per marble.

8.80 \div 22 = 0.40

The same one-unit idea applied to the supermarket bundle.

3Compare the unit prices

#7 Identify Subproblems 4.OA.A.2

Compare $0.45 and $0.40 per marble. Since $0.40 is less than $0.45, the supermarket sells marbles more cheaply.

0.45 > 0.40

Once both are measured per single marble, the smaller number is the better deal.

Answer: The supermarket (at $0.40 per marble versus $0.45 at the craft store).

4 · Reviewdoes it hold up?

Cross-check with equal counts: 396 marbles cost 22 x $8.10 = $178.20 at the craft store but 18 x $8.80 = $158.40 at the supermarket, so the supermarket is cheaper, agreeing with the per-marble result.

Another way: Identify subproblems (tool 7) by scaling to a common count: find the cost of 396 marbles at each store and compare $178.20 with $158.40 directly.

Standardsmin grade 4

4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison — Comparing the two stores by their per-marble unit prices.
4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing each total price by the number of marbles to get the unit price.

💡Takeaway. This only needs Grade 4 dividing -- find the price of one marble at each store, and the smaller one is the better deal!

Variant 5 medium answer: The supermarket (at $0.30 per marble versus $0.35 at the craft store).

A craft store sells $24$ marbles for $\$8.40$ , and a supermarket sells $16$ marbles for $\$4.80$ . Find which store sells the marbles more cheaply.

Show solution

1 · Understandwhat's really being asked

A craft store sells 24 marbles for $8.40 and a supermarket sells 16 marbles for $4.80. Find which store sells marbles more cheaply by comparing the price of a single marble.

Givens

Craft store: 24 marbles cost $8.40
Supermarket: 16 marbles cost $4.80
We want the cheaper store per marble

Unknowns

The price of one marble at each store, and which is lower

Constraints

Price per marble equals total price divided by the number of marbles
The cheaper store is the one with the smaller price per marble

2 · Planchoose the strategy

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

To compare bundles of different sizes fairly, reduce each to the same unit -- the price of one marble (dollars per marble) -- by dividing total price by count. The smaller per-marble price wins.

3 · Execute3 carry out the plan

1Price per marble at the craft store

#8 Analyze the Units 4.NBT.B.6

Divide the total by the number of marbles: $8.40 / 24 = $0.35 per marble.

8.40 \div 24 = 0.35

Splitting the total cost equally among 24 marbles gives the cost of just one.

2Price per marble at the supermarket

#8 Analyze the Units 4.NBT.B.6

Divide the total by the number of marbles: $4.80 / 16 = $0.30 per marble.

4.80 \div 16 = 0.30

The same one-unit idea applied to the supermarket bundle.

3Compare the unit prices

#7 Identify Subproblems 4.OA.A.2

Compare $0.35 and $0.30 per marble. Since $0.30 is less than $0.35, the supermarket sells marbles more cheaply.

0.35 > 0.30

Once both are measured per single marble, the smaller number is the better deal.

Answer: The supermarket (at $0.30 per marble versus $0.35 at the craft store).

4 · Reviewdoes it hold up?

Cross-check with equal counts: 384 marbles cost 16 x $8.40 = $134.40 at the craft store but 24 x $4.80 = $115.20 at the supermarket, so the supermarket is cheaper, agreeing with the per-marble result.

Another way: Identify subproblems (tool 7) by scaling to a common count: find the cost of 384 marbles at each store and compare $134.40 with $115.20 directly.

Standardsmin grade 4

4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison — Comparing the two stores by their per-marble unit prices.
4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing each total price by the number of marbles to get the unit price.

💡Takeaway. This only needs Grade 4 dividing -- find the price of one marble at each store, and the smaller one is the better deal!

Variant 6 medium answer: The craft store (at $0.20 per marble versus $0.30 at the supermarket).

A craft store sells $25$ marbles for $\$5.00$ , and a supermarket sells $18$ marbles for $\$5.40$ . Find which store sells the marbles more cheaply.

Show solution

1 · Understandwhat's really being asked

A craft store sells 25 marbles for $5.00 and a supermarket sells 18 marbles for $5.40. Find which store sells marbles more cheaply by comparing the price of a single marble.

Givens

Craft store: 25 marbles cost $5.00
Supermarket: 18 marbles cost $5.40
We want the cheaper store per marble

Unknowns

The price of one marble at each store, and which is lower

Constraints

Price per marble equals total price divided by the number of marbles
The cheaper store is the one with the smaller price per marble

2 · Planchoose the strategy

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

To compare bundles of different sizes fairly, reduce each to the same unit -- the price of one marble (dollars per marble) -- by dividing total price by count. The smaller per-marble price wins.

3 · Execute3 carry out the plan

1Price per marble at the craft store

#8 Analyze the Units 4.NBT.B.6

Divide the total by the number of marbles: $5.00 / 25 = $0.20 per marble.

5.00 \div 25 = 0.20

Splitting the total cost equally among 25 marbles gives the cost of just one.

2Price per marble at the supermarket

#8 Analyze the Units 4.NBT.B.6

Divide the total by the number of marbles: $5.40 / 18 = $0.30 per marble.

5.40 \div 18 = 0.30

The same one-unit idea applied to the supermarket bundle.

3Compare the unit prices

#7 Identify Subproblems 4.OA.A.2

Compare $0.20 and $0.30 per marble. Since $0.20 is less than $0.30, the craft store sells marbles more cheaply.

0.20 < 0.30

Once both are measured per single marble, the smaller number is the better deal.

Answer: The craft store (at $0.20 per marble versus $0.30 at the supermarket).

4 · Reviewdoes it hold up?

Cross-check with equal counts: 450 marbles cost 18 x $5.00 = $90.00 at the craft store but 25 x $5.40 = $135.00 at the supermarket, so the craft store is cheaper, agreeing with the per-marble result.

Another way: Identify subproblems (tool 7) by scaling to a common count: find the cost of 450 marbles at each store and compare $90.00 with $135.00 directly.

Standardsmin grade 4

4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison — Comparing the two stores by their per-marble unit prices.
4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing each total price by the number of marbles to get the unit price.

💡Takeaway. This only needs Grade 4 dividing -- find the price of one marble at each store, and the smaller one is the better deal!

Variant 7 medium answer: The supermarket (at $0.50 per marble versus $0.60 at the craft store).

A craft store sells $12$ marbles for $\$7.20$ , and a supermarket sells $30$ marbles for $\$15.00$ . Find which store sells the marbles more cheaply.

Show solution

1 · Understandwhat's really being asked

A craft store sells 12 marbles for $7.20 and a supermarket sells 30 marbles for $15.00. Find which store sells marbles more cheaply by comparing the price of a single marble.

Givens

Craft store: 12 marbles cost $7.20
Supermarket: 30 marbles cost $15.00
We want the cheaper store per marble

Unknowns

The price of one marble at each store, and which is lower

Constraints

Price per marble equals total price divided by the number of marbles
The cheaper store is the one with the smaller price per marble

2 · Planchoose the strategy

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

To compare bundles of different sizes fairly, reduce each to the same unit -- the price of one marble (dollars per marble) -- by dividing total price by count. The smaller per-marble price wins.

3 · Execute3 carry out the plan

1Price per marble at the craft store

#8 Analyze the Units 4.NBT.B.6

Divide the total by the number of marbles: $7.20 / 12 = $0.60 per marble.

7.20 \div 12 = 0.60

Splitting the total cost equally among 12 marbles gives the cost of just one.

2Price per marble at the supermarket

#8 Analyze the Units 4.NBT.B.6

Divide the total by the number of marbles: $15.00 / 30 = $0.50 per marble.

15.00 \div 30 = 0.50

The same one-unit idea applied to the supermarket bundle.

3Compare the unit prices

#7 Identify Subproblems 4.OA.A.2

Compare $0.60 and $0.50 per marble. Since $0.50 is less than $0.60, the supermarket sells marbles more cheaply.

0.60 > 0.50

Once both are measured per single marble, the smaller number is the better deal.

Answer: The supermarket (at $0.50 per marble versus $0.60 at the craft store).

4 · Reviewdoes it hold up?

Cross-check with equal counts: 360 marbles cost 30 x $7.20 = $216.00 at the craft store but 12 x $15.00 = $180.00 at the supermarket, so the supermarket is cheaper, agreeing with the per-marble result.

Another way: Identify subproblems (tool 7) by scaling to a common count: find the cost of 360 marbles at each store and compare $216.00 with $180.00 directly.

Standardsmin grade 4

4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison — Comparing the two stores by their per-marble unit prices.
4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing each total price by the number of marbles to get the unit price.

💡Takeaway. This only needs Grade 4 dividing -- find the price of one marble at each store, and the smaller one is the better deal!

Variant 8 hard answer: The supermarket (at $0.35 per marble versus $0.40 at the craft store).

A craft store sells $35$ marbles for $\$14.00$ , and a supermarket sells $28$ marbles for $\$9.80$ . Find which store sells the marbles more cheaply.

Show solution

1 · Understandwhat's really being asked

A craft store sells 35 marbles for $14.00 and a supermarket sells 28 marbles for $9.80. Find which store sells marbles more cheaply by comparing the price of a single marble.

Givens

Craft store: 35 marbles cost $14.00
Supermarket: 28 marbles cost $9.80
We want the cheaper store per marble

Unknowns

The price of one marble at each store, and which is lower

Constraints

Price per marble equals total price divided by the number of marbles
The cheaper store is the one with the smaller price per marble

2 · Planchoose the strategy

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

To compare bundles of different sizes fairly, reduce each to the same unit -- the price of one marble (dollars per marble) -- by dividing total price by count. The smaller per-marble price wins.

3 · Execute3 carry out the plan

1Price per marble at the craft store

#8 Analyze the Units 4.NBT.B.6

Divide the total by the number of marbles: $14.00 / 35 = $0.40 per marble.

14.00 \div 35 = 0.40

Splitting the total cost equally among 35 marbles gives the cost of just one.

2Price per marble at the supermarket

#8 Analyze the Units 4.NBT.B.6

Divide the total by the number of marbles: $9.80 / 28 = $0.35 per marble.

9.80 \div 28 = 0.35

The same one-unit idea applied to the supermarket bundle.

3Compare the unit prices

#7 Identify Subproblems 4.OA.A.2

Compare $0.40 and $0.35 per marble. Since $0.35 is less than $0.40, the supermarket sells marbles more cheaply.

0.40 > 0.35

Once both are measured per single marble, the smaller number is the better deal.

Answer: The supermarket (at $0.35 per marble versus $0.40 at the craft store).

4 · Reviewdoes it hold up?

Cross-check with equal counts: 980 marbles cost 28 x $14.00 = $392.00 at the craft store but 35 x $9.80 = $343.00 at the supermarket, so the supermarket is cheaper, agreeing with the per-marble result.

Another way: Identify subproblems (tool 7) by scaling to a common count: find the cost of 980 marbles at each store and compare $392.00 with $343.00 directly.

Standardsmin grade 4

4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison — Comparing the two stores by their per-marble unit prices.
4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing each total price by the number of marbles to get the unit price.

💡Takeaway. This only needs Grade 4 dividing -- find the price of one marble at each store, and the smaller one is the better deal!

Variant 9 hard answer: The craft store (at $0.25 per marble versus $0.30 at the supermarket).

A craft store sells $40$ marbles for $\$10.00$ , and a supermarket sells $24$ marbles for $\$7.20$ . Find which store sells the marbles more cheaply.

Show solution

1 · Understandwhat's really being asked

A craft store sells 40 marbles for $10.00 and a supermarket sells 24 marbles for $7.20. Find which store sells marbles more cheaply by comparing the price of a single marble.

Givens

Craft store: 40 marbles cost $10.00
Supermarket: 24 marbles cost $7.20
We want the cheaper store per marble

Unknowns

The price of one marble at each store, and which is lower

Constraints

Price per marble equals total price divided by the number of marbles
The cheaper store is the one with the smaller price per marble

2 · Planchoose the strategy

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

To compare bundles of different sizes fairly, reduce each to the same unit -- the price of one marble (dollars per marble) -- by dividing total price by count. The smaller per-marble price wins.

3 · Execute3 carry out the plan

1Price per marble at the craft store

#8 Analyze the Units 4.NBT.B.6

Divide the total by the number of marbles: $10.00 / 40 = $0.25 per marble.

10.00 \div 40 = 0.25

Splitting the total cost equally among 40 marbles gives the cost of just one.

2Price per marble at the supermarket

#8 Analyze the Units 4.NBT.B.6

Divide the total by the number of marbles: $7.20 / 24 = $0.30 per marble.

7.20 \div 24 = 0.30

The same one-unit idea applied to the supermarket bundle.

3Compare the unit prices

#7 Identify Subproblems 4.OA.A.2

Compare $0.25 and $0.30 per marble. Since $0.25 is less than $0.30, the craft store sells marbles more cheaply.

0.25 < 0.30

Once both are measured per single marble, the smaller number is the better deal.

Answer: The craft store (at $0.25 per marble versus $0.30 at the supermarket).

4 · Reviewdoes it hold up?

Cross-check with equal counts: 960 marbles cost 24 x $10.00 = $240.00 at the craft store but 40 x $7.20 = $288.00 at the supermarket, so the craft store is cheaper, agreeing with the per-marble result.

Another way: Identify subproblems (tool 7) by scaling to a common count: find the cost of 960 marbles at each store and compare $240.00 with $288.00 directly.

Standardsmin grade 4

4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison — Comparing the two stores by their per-marble unit prices.
4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing each total price by the number of marbles to get the unit price.

💡Takeaway. This only needs Grade 4 dividing -- find the price of one marble at each store, and the smaller one is the better deal!

Variant 10 hard answer: The craft store (at $0.25 per marble versus $0.30 at the supermarket).

A craft store sells $50$ marbles for $\$12.50$ , and a supermarket sells $32$ marbles for $\$9.60$ . Find which store sells the marbles more cheaply.

Show solution

1 · Understandwhat's really being asked

A craft store sells 50 marbles for $12.50 and a supermarket sells 32 marbles for $9.60. Find which store sells marbles more cheaply by comparing the price of a single marble.

Givens

Craft store: 50 marbles cost $12.50
Supermarket: 32 marbles cost $9.60
We want the cheaper store per marble

Unknowns

The price of one marble at each store, and which is lower

Constraints

Price per marble equals total price divided by the number of marbles
The cheaper store is the one with the smaller price per marble

2 · Planchoose the strategy

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

To compare bundles of different sizes fairly, reduce each to the same unit -- the price of one marble (dollars per marble) -- by dividing total price by count. The smaller per-marble price wins.

3 · Execute3 carry out the plan

1Price per marble at the craft store

#8 Analyze the Units 4.NBT.B.6

Divide the total by the number of marbles: $12.50 / 50 = $0.25 per marble.

12.50 \div 50 = 0.25

Splitting the total cost equally among 50 marbles gives the cost of just one.

2Price per marble at the supermarket

#8 Analyze the Units 4.NBT.B.6

Divide the total by the number of marbles: $9.60 / 32 = $0.30 per marble.

9.60 \div 32 = 0.30

The same one-unit idea applied to the supermarket bundle.

3Compare the unit prices

#7 Identify Subproblems 4.OA.A.2

Compare $0.25 and $0.30 per marble. Since $0.25 is less than $0.30, the craft store sells marbles more cheaply.

0.25 < 0.30

Once both are measured per single marble, the smaller number is the better deal.

Answer: The craft store (at $0.25 per marble versus $0.30 at the supermarket).

4 · Reviewdoes it hold up?

Cross-check with equal counts: 1600 marbles cost 32 x $12.50 = $400.00 at the craft store but 50 x $9.60 = $480.00 at the supermarket, so the craft store is cheaper, agreeing with the per-marble result.

Another way: Identify subproblems (tool 7) by scaling to a common count: find the cost of 1600 marbles at each store and compare $400.00 with $480.00 directly.

Standardsmin grade 4

4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison — Comparing the two stores by their per-marble unit prices.
4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing each total price by the number of marbles to get the unit price.

💡Takeaway. This only needs Grade 4 dividing -- find the price of one marble at each store, and the smaller one is the better deal!