A summer camp is organizing a hike and needs to buy granola bars for the campers. The granola bars come in small boxes and large boxes. Each small box has 10 granola bars and each large box has 24 granola bars. The camp bought a total of 17 boxes that have 296 granola bars altogether. Write a system of equations that could be used to determine the number of small boxes purchased and the number of large boxes purchased. Define the variables that you use to write the system.

The Answer is: There are 8 small boxes and 9 large boxes. See explanation below for variables and variable definitions.

Step-by-step explanation:

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

s + b = 17

You can solve for s:

s = 17 - b

You can solve for b:

b = 17 - s

10 times the number of small boxes plus 24 times the number of large boxes is equal to 296 granola bars.

10s + 24b = 296

Substitute:

10 (17 - b) + 24b = 296

170 - 10b + 24b = 296

14b = 296 - 170

14b = 126

b = 126 / 14 = 9 large boxes

Find the number of small boxes, s:

s = 17 - b = 17 - 9 = 8 small boxes

There are 8 small boxes and 9 large boxes.

Proof:

10 (8) + 24 (9) = 296

80 + 216 = 296

296 = 296