A summer camp is organizing a hike in needs to buy granola bars for the campers. The granola bars come in small boxes in large boxes. Each small box has 8 granola bars in each large bags as 12 granola bars. The camp by twice times as many small boxes as large boxes, which are together has 56 granola bars. Determine the number of small boxes purchased and the number of large boxes purchased

The number of large boxes of granola bars = 2

The number of small boxes of granola bars = 4 boxes.

Step-by-step explanation:

The number of granola bars in each small box = 8

The number of bars in each large bag = 12 bars

Now, total number of granola bars in the total bags = 56

Let us assume the number of large boxes in the camp = m

So, the number of small boxes = 2 x (Number of large boxes) = 2 x (m) = 2 m

Also, number of granola bars in m large boxes

= m x (Number of bars in 1 large bag) = m x (12) = 12 m

And, number of granola bars in 2 m small boxes

= 2 m x (Number of bars in 1 small bag) = 2 m x (8) = 16 m

⇒ Total number of bars in (large + small) box = Total bars

⇒ 12 m + 16 m = 56

or, 28 m = 56

or, m = 56/28 = 2, or m = 2

Hence, the number of large boxes of granola bars = m = 2

The number of small boxes of granola bars = 2 m = 2 x 2 = 4 boxes.