Question

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?

Answer 1

`4` ounces of cheese

Explanation:

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

Let's make a ratio of these two statements:

`1/3 : 1/12`

This is saying that for every `1/3` of an `color(red)(o u n c e` we have `1/12` of a `color(blue)(pound)`. Uh-oh, those units don't match. Let's make them match before things get confusing

To go from `1/3` ounces to pounds, we need to divide by `16`. That gives us `1/48` `color(blue)(pounds)` instead of `1/3` ounces

So now our ratio is `1/48 : 1/12`

We are looking for how much cheese we need when we have a pound of pizza. So, we need to make `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 xx 1/48 : 1/12 xx 12`

or `12/48 : 1`

or `1/4 : 1`

We are almost done! This ratio says that for every `1/4` `color(blue)(pound` of cheese we have `1` `color(blue)(pound)` of pizza. However, our final answer is supposed to be in ounces.

So we convert again, multiplying `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