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 8 granola bars and each large box has 12 granola bars. The camp bought 3 times as many small boxes as large boxes, which altogether had 72 granola bars. 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.
Question
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 8 granola bars and each large box has 12 granola bars. The camp bought 3 times as many small boxes as large boxes, which altogether had 72 granola bars. 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.
Solution
Let's define the variables first:
Let S be the number of small boxes purchased. Let L be the number of large boxes purchased.
From the problem, we know that each small box has 8 granola bars and each large box has 12 granola bars. We also know that the total number of granola bars is 72. This gives us our first equation:
8S + 12L = 72
We also know from the problem that the camp bought 3 times as many small boxes as large boxes. This gives us our second equation:
S = 3L
So, the system of equations is:
8S + 12L = 72 S = 3L
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