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# Mixing Lemonade Poster

**Answer**: the first glass tasted stronger
**How do you know?**
__Method 1: making the same amount of lemon juice__
__Method 2: making the same amount of water__
__Method 3: scaling lemon juice to water__
__Method 4: fractions__
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Age 11 to 14

Challenge Level

- Problem
- Student Solutions

First glass lemon:water 60:200

Second glass lemon:water 100:350

60$\times$5 = 100$\times$3 = 300

200$\times$5 = 1000, so first glass lemon:water 300:1000

350$\times$3 = 1050, so second glass lemon:water 300:1050

First glass has less water for the same amount of lemon juice so the first glass tastes stronger.

First glass lemon:water 60:200

Second glass lemon:water 100:350

200$\times$7 = 350$\times$4 = 1400

60$\times$7 = 420, so first glass lemon:water 420:1400

100$\times$4 = 400, so second glass lemon:water 400:1400

First glass has more lemon juice for the same amount of water so the first glass tastes stronger.

First glass: scale factor from lemon juice to water is 3.333

Second glass: scale factor from lemon juice to water is 3.5

There is more water compared to lemon juice in the second glass, so the first glass tastes stronger.

First glass: $\frac{60}{260} =\frac6{26} = \frac3{13}$ lemon juice

Second glass: $\frac{100}{450} = \frac{10}{45} = \frac29$ lemon juice

Common denominator: $13\times9$

First glass: $\frac3{13} = \frac{27}{13\times9}$

Second glass: $\frac27 = \frac{26}{13\times9}$

The first glass has a greater fraction of lemon juice so it tastes stronger.