Dillard

2021-02-25

Nancy and Warren are making large pots of chicken noodle soup. Nancy opens 4 large cans and 6 small cans of soup and pours them into her pot. Her pot contains 115 ounces of soup. Warren opens 3 large cans and 5 small cans of soup. His pot contains 91 ounces of soup. How many ounces of soup does each large can and each small can contain?

Let l be the number of ounce of soup in the large can and s be the number of ounce of soup in the small can.
4 large cans and 6 small cans of soup is equal to 115 ounces of soup:

$41+6s=115$

3 large cans and 5 small cans of soup is equal to 91 ounces of soup:

$3l+5s=91$

Solve by elimination. Here, I eliminated first. Multiply (1) by 5 to obtain (3):

$20l+30s=575$

Multiply (2) by 6 to obtain (4):

$18l+30s=546$

Subtract each sides of (3) and (4) and solve for l:

$2l=29$

$l=14.5$

Solve for 2 using (1):

$4\left(145\right)+6s=115$

$58+6s=115$

$6s=57$

$s=9.5$

So, a large can contains 14.5 ounces of soup and a small can contains 9.5 ounces of soup.

Jeffrey Jordon