Question

1. use a proportion to find each value.

a. 2% of 180
\\(\frac{n}{\square}=\frac{2}{\square}\\)
b. what percent is 17 out of 40?
\\(\frac{\square}{\square}=\frac{p}{\square}\\)

Explanation:

Step1: Set up proportion for part a

The proportion for finding a percentage of a number is $\frac{n}{180}=\frac{2}{100}$, where $n$ is the part we want to find, 180 is the whole number, and 2 is the percentage out of 100.

Step2: Solve for $n$ in part a

Cross - multiply: $100n = 2\times180$, so $100n=360$, then $n=\frac{360}{100}=3.6$.

Step3: Set up proportion for part b

The proportion for finding what percent one number is of another is $\frac{17}{40}=\frac{p}{100}$, where 17 is the part, 40 is the whole, and $p$ is the percentage we want to find.

Step4: Solve for $p$ in part b

Cross - multiply: $40p=17\times100$, so $40p = 1700$, then $p=\frac{1700}{40}=42.5$.

Answer:

a. $\frac{n}{180}=\frac{2}{100}$, $n = 3.6$
b. $\frac{17}{40}=\frac{p}{100}$, $p = 42.5$