Question

Owen is making lemonade from concentrate. The number of quarts of water he needs is 4 times the number of quarts of concentrate. How many quarts of water and how many quarts of concentrate does Owen need to make 100 quarts of lemonade?

Short answer

He needs 80 quarts of water and 20 quarts of concentrate.

Step-by-step solution

Given

Owen is making lemonade from concentrate. The number of quarts of water he needs is 4 times the number of quarts of concentrate.

To determine

How many quarts of water and how many quarts of concentrate does Owen need to make 100 quarts of lemonade?

Calculation

Let,

He needs x quarts of water and y quarts of concentrate.

According to the question:

$$\begin{gathered} x=4y \\ x+y=100 \end{gathered}$$

Plug $x=4y$in the other equation.

$$\begin{gathered} x+y=100 \\ 4y+y=100 \\ 5y=100 \\ y=20 \\ 4y=80 \end{gathered}$$

Hence, he needs 80 quarts of water and 20 quarts of concentrate.