Question

John knows that a good coffee needs a cup of water for every 2 cups of milk. If so, find the missing values in the following recipe for different amounts of coffee.

• A. A = 6 ; B = 5 ; C = 14
• B. A = 6 ; B = 5 ; C = 15
• C. A = 12 ; B = 5 ; C = 21
• D. A = 5 ; B = 6 ; C = 14

Answer 1

The correct option is A A = 6 ; B = 5 ; C = 14

$\text{Ratio of water to milk}=1:2$

$\text{The ratio 1:2 can be expressed as the}\text{fraction}\frac{1}{2}$

$\text{Multiplying the numerator and the}\text{denominator by 3, we get:}$

$\frac{1}{2}=\frac{1\times 3}{2\times 3}=\frac{3}{6}$

$\therefore \text{For 3 cups of water, the corresponding}$ $\text{amount of milk added to the coffee is 6}\text{cups.}$

$⟹A=6$

$\text{Similarly, multiplying the numerator and}\text{the denominator by 5, we get:}$

$\frac{1}{2}=\frac{1\times 5}{2\times 5}=\frac{5}{10}$

$\therefore \text{For 10 cups of milk, the corresponding}$ $\text{amount of water added to the coffee is 5}\text{cups.}$

$⟹B=5$

$\text{Finally, multiplying the numerator and}\text{the denominator by 7, we get:}$

$\frac{1}{2}=\frac{1\times 7}{2\times 7}=\frac{7}{14}$

$\therefore \text{For 7 cups of water, the corresponding}$ $\text{amount of milk added to the coffee is 14}\text{cups.}$

$⟹C=14$