# You can buy 5 stickers for 3 dollars. What's the proportion that gives the cost if you buy 12 stickers?

Apr 20, 2018

See below.

#### Explanation:

First of all, a proportion is $\frac{\textcolor{g r e e n}{x}}{\textcolor{b l u e}{y}} = \frac{\textcolor{g r e e n}{x}}{\textcolor{b l u e}{y}}$. This is like comparing two things.

So, you know already that one part of your proportion is going to be $\frac{\textcolor{g r e e n}{5}}{\textcolor{b l u e}{3}}$ because of $\textcolor{g r e e n}{5}$ stickers, and $\textcolor{b l u e}{3}$ dollars. Now think about what you know for the second part of the proportion. You know the number of stickers. And since these two fractions are being set next to each other, the sticker quantity must be in the same spot in both fractions. But, since you don't know the cost, we are going to replace that with your variable, $x$.

Now, put that all together, and we are left with $\frac{\textcolor{g r e e n}{5}}{\textcolor{b l u e}{3}} = \frac{\textcolor{g r e e n}{12}}{\textcolor{b l u e}{x}}$. That is your proportion.

If you want to solve this, you would have to cross multiply. So, you would do $\textcolor{g r e e n}{5} \cdot \textcolor{b l u e}{x}$ and $\textcolor{g r e e n}{12} \cdot \textcolor{b l u e}{3}$. Then, you simplify, and are left with $5 x = 36$. To find $x$, or the cost, you must isolate the variable. So, divie 5 from both sides.

$\frac{5 x}{5} = \frac{36}{5}$

Simplify, and you are left with $x = 7.5$. This means that for 12 stickers, the cost is \$7.50.