Mixing Lemonade Poster

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.