Question

Yuan has 5 quarts of broth. He uses 1/2 of the broth to make soup. Then, he uses 1/4 of the broth he has left to make gravy.

How much broth, in quarts, does Yuan have left after making soup and gravy?

Answer 1

1 7/8 quarts

Explanation:

The amount Yuan has left can be found by multiplying the original amount by the fraction he has left.

__

used

After using 1/2 of the broth for soup, the fraction remaining is ...

1 -1/2 = 1/2

The amount Yuan used for gravy is 1/4 of this, or ...

(1/4)(1/2) = 1/8 . . . of the original amount of broth

The total fraction Yuan used was ...

fraction used = fraction for soup + fraction for broth = 1/2 +1/8 = 5/8

remaining

Then the fraction remaining is ...

fraction remaining = 1 - fraction used = 1 - 5/8 = 3/8.

The amount remaining is this fraction of the original amount:

(3/8)(5 quarts) = 15/8 quarts = 1 7/8 quarts . . . . remaining