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.

Answer 1

To determine the number of small boxes and large boxes purchased, set up a system of equations using the given information. Solve the system to find the values of x and y. The camp purchased 6 small boxes and 2 large boxes.

Step-by-step explanation:

To determine the number of small boxes purchased and the number of large boxes purchased, we can set up a system of equations using the given information. Let's define our variables:

Let x be the number of small boxes.

Let y be the number of large boxes.

From the problem, we know that:

x = 3y (The camp bought 3 times as many small boxes as large boxes)

8x + 12y = 72 (Altogether, the boxes had 72 granola bars)

Now we can solve this system of equations to find the values of x and y.

Substituting the value of x from the first equation into the second equation, we have:

8(3y) + 12y = 72

24y + 12y = 72

36y = 72

y = 2

Substituting y = 2 back into the first equation, we have:

x = 3(2)

x = 6

Therefore, the camp purchased 6 small boxes and 2 large boxes.

Answer 2

8x + 12y = 72

3y = x

Step-by-step explanation:

If we set small boxes as x and large boxes as y, then...

8x + 12y = 72

y = x/3 or 3y = x

It's just reading the problem, nothing to explain here.