Find the per-unit-weight rate first

3.OA.A.33.MD.A.2 · adapt · grade 3

Archetype: Multiplicative Comparison and Unit Rate · step in a 7-type progression

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

Show solution

Understand

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 (= 1.5 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: $4 per 8 oz of tomatoes;$ 9 per 1 lb of pork.
Money amounts are in dollars and cents.

Plan

#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.

Execute

#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

16 \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.

#7 Identify Subproblems 3.OA.A.3

1 lb 8 oz is one whole pound plus half a pound (8 oz = half of 16 oz). At

9 per pound, one pound costs

9 and the extra half-pound costs half of

9, which is

4.50.

\$9 + \tfrac{1}{2}\times\$9 = \$9 + \$4.50 = \$13.50

Recognizing 8 oz as half a pound and taking half of the per-pound price is a within-100 multiplication/division word-problem skill.

#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

Combining the two subtotals is a single addition of two money amounts.

Answer: $21.50

Review

Tomatoes $8 and pork$ 13.50 are both sensible store prices, and $13.50 >$ 8 makes sense because pork is heavier (1.5 lb) and pricier per unit. The total $21.50 is between$ 20 and $25, a reasonable grocery sum.

Use Guess and Check on the half-pound: confirm that half of $9 is$ 4.50 because $4.50 +$ 4.50 = $9, then add$ 8 + $9 +$ 4.50.

Standards · min grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting 1 lb to 16 oz 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.

💡 Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!