Question

Timmy uses 1 1 2 cups of sugar for every 2 gallons of lemonade he makes. How many cups of sugar would Timmy use if he makes 13 gallons of lemonade?

Answer 1

$\bf \begin{array}{ccll} \stackrel{sugar}{cups}&\stackrel{lemonade}{gallons}\\ \cline{1-2}\\[0.25em] 1\frac{1}{2}&2\\ x&13 \end{array}\implies \cfrac{~~1\frac{1}{2}~~}{x}=\cfrac{2}{13}\implies \cfrac{~~\frac{3}{2}~~}{\frac{x}{1}}=\cfrac{2}{13}\implies \cfrac{3}{2}\cdot \cfrac{1}{x}=\cfrac{2}{13} \\\\\\ \cfrac{3}{2x}=\cfrac{2}{13}\implies 39=4x\implies \cfrac{39}{4}=x\implies 9\frac{3}{4}=x$

Answer 2

Answer:

9 3/4 cups

Step-by-step explanation:

This is an example of direct variation where the relationship of 2 elements is such that the increase in one results in an increase in the other. From the question, the increase in the gallons of lemonade made would result in an increase in the number of sugar used.

Given that Timmy uses 1 1/2 cups of sugar for every 2 gallons of lemonade he makes

Let the number of cups of sugar used be x and the number of gallons of lemonade be y

then x α y

x = ky

3/2 = k(2)

k = 3/4

x = 3k/4

To make 13 gallons of lemonade,

x = 3 × 13/4

x = 39/4 = 9 3/4

Timmy would use 9 3/4 cups of sugar to 13 gallons of lemonade.