Find the value of one unit

4.NBT.B.64.OA.A.2 · adapt · grade 4

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

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

Understand

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

Plan

#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.

Execute

#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.

#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.

#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.

0.30 < 0.35

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).

Review

Cross-check with equal counts: 48 marbles cost 2 x $8.40 =$ 16.80 at the craft store but 3 x $4.80 =$ 14.40 at the supermarket, so the supermarket is cheaper, agreeing with the per-marble result.

Identify subproblems (tool 7) by scaling to a common count: find the cost of 48 marbles at each store (LCM of 24 and 16) and compare $16.80 with$ 14.40 directly.

Standards · min 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.

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