Question

A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 2 large boxes and 5 small boxes has a total weight of 77 kilograms. A delivery of 8 large boxes and 3 small boxes has a total weight of 104 kilograms. How much does each type of box weigh?

Answer 1

The answer is that large boxes are 8.5 kilograms and small boxes are 12 kilograms.

Explanation:

Let l = large boxes and s = small boxes.

Delivery 1:

2 large boxes plus 5 small boxes = 77 kilograms

2l + 5s = 77 kilograms

The 8 large boxes plus 3 small boxes = 104 kilograms

8l + 3s = 104 kilograms

Solve for l:

8l = -3s + 104

l = -3/8s + 104/8

l = -3/8s + 13

Substitute:

2l + 5s = 77

2(-3/8s + 13) + 5s = 77

-6/8s + 26 + 5s = 77

--6/8s + 5s = 77 - 26

-6/8s + 40/8s = 51

34/8s = 51

s = 51 * 8/34 = 408/34 = 12 kilograms for small boxes

l = -3/8s + 13 = -3/8(12) + 13 = -36/8 + 104/8 = 68/8 = 8.5 kilograms

Proof 1:

8l + 3s = 104

8(8.5) + 3(12) = 104

68 + 36 = 104

104 = 104

Proof 2:

2l + 5s = 77

2(8.5) + 5(12) = 77

17 + 60 = 77

77 = 77

Hope this helps! Have a great day!