Sara sold 22 large and small boxes of oranges. Small boxes cost $4 and large boxes cost $12 for a total of $200. How many of each small boxes and large boxes were sold?

The Answer is: There were 8 small boxes and 14 large boxes.

Step-by-step explanation:

Let s = small boxes and let b = large boxes.

s + b = 22

Solve for s:

s = 22 - b

$4 times the number of small boxes plus $12 times the number of large boxes is equal to $200. Set up the equation:

4 (s) + 12 (b) = 200

Substitute:

4 (22 - b) + 12b = 200

88 - 4b + 12b = 200

88 + 8b = 200

8b = 112

b = 14 large boxes

Now solve for the number of small boxes:

s = 22 - b

s = 22 - 14 = 8 small boxes

There were 8 small boxes and 14 large boxes.

Proof:

4 (s) + 12 (b) = 200

4 (8) + 12 (14) = 200

32 + 168 = 200

200 = 200