# Sophia used 1/3 of an ounce of cheese to make 1/12 of a pound of pizza dough. How l many ounces of cheese are needed to make a pound of pizza dough?

Jan 2, 2018

$4$ ounces of cheese

#### Explanation:

Note: One pound is the same as $16$ ounces

Let's make a ratio of these two statements:

$\frac{1}{3} : \frac{1}{12}$

This is saying that for every $\frac{1}{3}$ of an color(red)(o u n c e we have $\frac{1}{12}$ of a $\textcolor{b l u e}{p o u n d}$. Uh-oh, those units don't match. Let's make them match before things get confusing

To go from $\frac{1}{3}$ ounces to pounds, we need to divide by $16$. That gives us $\frac{1}{48}$ $\textcolor{b l u e}{p o u n \mathrm{ds}}$ instead of $\frac{1}{3}$ ounces

So now our ratio is $\frac{1}{48} : \frac{1}{12}$

We are looking for how much cheese we need when we have a pound of pizza. So, we need to make $\frac{1}{12}$ lbs of pizza into
$1$ lb of pizza. We do this by multiplying by $12$.

BUT we need to do the same on the other side

So now we have $12 \times \frac{1}{48} : \frac{1}{12} \times 12$

or $\frac{12}{48} : 1$

or $\frac{1}{4} : 1$

We are almost done! This ratio says that for every $\frac{1}{4}$ color(blue)(pound of cheese we have $1$ $\textcolor{b l u e}{p o u n d}$ of pizza. However, our final answer is supposed to be in ounces.

So we convert again, multiplying $\frac{1}{4}$ by $16$, which gives us $4$ ounces.

So, if you have $1$ pound of pizza, you must have used $4$ ounces of cheese