Add poured water to find total capacity

3.MD.A.2 · adapt · grade 3

Archetype: Track a Quantity Through Changes · step in a 7-type progression

Mrs. Carter has a jug holding $11\ \text{cups}\ 2\ \text{fl oz}$ of lemonade. She fills a small cup to the brim with lemonade and pours it into the jug $5$ more times. If the jug now holds $13\ \text{cups}\ 1\ \text{fl oz}$ of lemonade, what is the capacity of the small cup, in fluid ounces? (Note: $1\ \text{cup} = 8\ \text{fl oz}$ .)

Show solution

Understand

A jug starts with 11 cups 2 fl oz of lemonade. A small cup of lemonade is filled to the brim and poured in 5 times. The jug then holds 13 cups 1 fl oz. Find the capacity of the small cup in fluid ounces, where 1 cup = 8 fl oz.

Givens

Starting amount in the jug is 11 cups 2 fl oz.
Ending amount in the jug is 13 cups 1 fl oz.
A full small cup is poured in 5 times.
1 cup = 8 fl oz.

Unknowns

The capacity of the small cup in fluid ounces.

Constraints

The small cup is filled to the brim each time, so all 5 pours are equal.

Plan

#8 Analyze the Units · also uses: #11 Work Backwards

Convert both amounts to fluid ounces, subtract to find the total amount poured in, then divide that by 5 equal pours to get the small cup's capacity.

Execute

#8 Analyze the Units 3.MD.A.2

Since 1 cup = 8 fl oz, the start 11 cups 2 fl oz = 11 x 8 + 2 = 90 fl oz, and the end 13 cups 1 fl oz = 13 x 8 + 1 = 105 fl oz.

11 \times 8 + 2 = 90,\quad 13 \times 8 + 1 = 105

Using one unit (fluid ounces) makes the added amount easy to find.

#11 Work Backwards 3.MD.A.2

The jug grew from 90 fl oz to 105 fl oz, so the 5 pours added 105 - 90 = 15 fl oz altogether.

105 - 90 = 15\ \text{fl oz}

The increase in the jug is exactly what the small cup added in total.

#8 Analyze the Units 3.OA.A.3

All 5 pours were equal full cups, so each cup holds 15 divided by 5 = 3 fl oz.

15 \div 5 = 3\ \text{fl oz}

Sharing the 15 fl oz into 5 equal pours gives the size of one cup.

Answer: 3 fl oz

Review

Five cups of 3 fl oz add 5 x 3 = 15 fl oz, and 90 + 15 = 105 fl oz = 13 cups 1 fl oz, which matches the final amount, so 3 fl oz is correct.

Make a systematic list (tool 2): after each pour of 3 fl oz the jug holds 93, 96, 99, 102, 105 fl oz, reaching 105 fl oz after the 5th pour.

Standards · min grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting cup-and-ounce volumes and finding the added amount.
3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing the total added volume by 5 equal pours.

💡 This only needs Grade 3 sense: find how much the jug grew, then split it into 5 equal cups!