Question

A farmer is selling fruit at his stand. On

Saturday he sold 10 small boxes of oranges
and 3 large boxes of oranges for $217. On
Sunday he sold 3 small boxes of oranges
and 12 large boxes of oranges for $276.
Find the cost of one small box and one
Targe box of oranges.

Answer 1

A large box costs $19.

A small box costs $16

Explanation:

s = cost of a small box

l = cost of a large box

From the problem, we can make these two formulas.

# of small boxes + # of large boxes = total cost

10s + 3l = 217

3s + 12l = 276

Rewrite one equation for either s or l:

3s = 276 - 12l

s = 92 - 4l

Now use substitution to solve. Plug the s equation from above into

10s + 3l = 217

10 (92 - 4l) + 3l = 217

920 - 40l + 3l = 217

-37l = -703

l = 19

This is the cost of a large box.

Plug l into:

s = 92 - 4l

s = 92 - 4(19)

s = 16

This is the cost of a small box.