word problem with fraction

Question

Ashley is making pancakes.  The recipe calls for 3/4 cups of milk to make 9 pancakes.  How many cups of milk will Hannah need in order to make 12 pancakes?

Answer 1

Heather,

 

I feel for you on this one! Whoever wrote it switched from Ashley to Hannah--I guess we're supposed to assume that's a mistake and they're actually the same person (otherwise, who knows?  Maybe Hannah uses a different recipe from Ashley's!).

 

But this question is about fractions and ratios, solved algebraically.  

 

1)  Let p = cups of milk required for one pancake

2)  So: 3/4 = 9p

3)  Then, we divide 3/4 by 9, or multiple by the reciprocal 1/9, so: 3/4 * 1/9 = p

4)  We simplify by factoring out "3," so: 1/4 * 1/3 = p

5)  p = 1/12

6)  Now, we know we're going to make 12 pancakes, so:  12 * p = our answer

7)  So:  12 * 1/12 = 1 cup of milk

 

That's it!