Mixing Lemonade Poster
Mixing Lemonade Poster
Age
11 to 14
Challenge level
This poster is based on the problem Mixing Lemonade.
The poster is available as a PDF, or the image below can be clicked on to enlarge it.
The poster is available as a PDF, or the image below can be clicked on to enlarge it.
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Answer: the first glass tasted stronger
How do you know?
Method 1: making the same amount of lemon juice
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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$3 = 1050, so second glass lemon:water 300:1050
First glass has less water for the same amount of lemon juice so the first glass tastes stronger.
Method 2: making the same amount of water
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First glass lemon:water 60:200
Second glass lemon:water 100:350
200$\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.
Method 3: scaling lemon juice to water
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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.
Method 4: fractions
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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.