In a jar, the ratio of the number of oatmeal cookies to the number of chocolate chip cookies is 5:2. If there are 20 oatmeal cookies, the number of chocolate chip cookies in the jar is
(A) 28
(B) 50
(C) 8
(D) 12
(E) 18
In a jar, the ratio of the number of oatmeal cookies to the number of chocolate chip cookies is 5:2. If there are 20 oatmeal cookies, the number of chocolate chip cookies in the jar is
(A) 28
(B) 50
(C) 8
(D) 12
(E) 18

## Solution

The ratio $5: 2$ indicates that there are 5 oatmeal cookies for every 2 chocolate chip cookies. Since there are 20 oatmeal cookies, there are four groups of 5 oatmeal cookies. Thus there are $4 ¥ 2=8$ chocolate chip cookies.

Algebraically, we could let $x$ represent the number of chocolate chip cookies. Then $5: 2=20: x$, or $\frac{5}{2}=\frac{20}{x}$. If we want to write $\frac{5}{2}$ as a fraction with a numerator of 20 , we multiply both the nu2
merator and denominator by
4 , ie. $\frac{5}{2}=\frac{5 \not 4}{2 ¥ 4}=\frac{20}{8}$. Therefore, $x=8$.

ANswer: (C)