## 5-B-1: The Magic of Proportions

It takes one large pizza of 8 slices to feed three adults. This weekend, we are having 12 adults over to watch football. How many large pizzas’ should we buy to feed everyone?

I would write the ratio for 3 adults as such

8 slices = x amount of slices

3 adults 12 adults

In order to find out how many slices of pizza we need, we can cross multiply 8 slices by 12 adults to get 96. We could then cross multiply 3 adults with “x” slices to get 3x. Next, set up the equation 3x=96 to find that we would need 32 slices of pizza. We could take it one step further to find out how many pizzas that would be by setting up a unit rate of 1 pizza feeds 3 adults so “x” pizzas feed 12 adults. Which if we followed the steps earlier we would know we need 4 pizzas.

Problem 2

It takes 2 bags of peanuts to make twelve cookies. How many bags would we need to buy to make 48 cookies? Set up the proportion as follows.

2 bags = x bags

12 cookies 48 cookies

To solve: Cross multiply 2 bags times 48 cookies and cross multiply 12 cookies by “x” bags. To get the equation 12x=96. “X” would then equal 8, so by substituting this in for x we find we would need 8 bags.

October 17, 2009 at 3:41 am

I noticed that you labeled the numbers that were used with the proportion (bags, cookies, slices, adults). That seems to help students when they set up proportions. Otherwise they can sometimes get mixed up what number goes on top or bottom, and where the x goes. Nice explanation.

Lou Ann