Question

A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 5 large boxes and 6 small boxes has a total weight of 175 kilograms. A delivery of 3 large boxes and 2 small boxes has a total weight of 83 kilograms. How much does each type of box weigh?

Weight of each large box: - kilogram(s)
Weight of each small box: - kilogram(s)

Answer 1

Set up two equations:

5L + 6S = 175

3L + 2S = 83

Multiply the second equation by -3:

-9L -6S = -249

Now add the first and 3rd equations together:

5L + 6S = 175 + -9L -6s = -249

-4L = -74

Divide both sides by -4:

L = -74 / -4 = 18.5

Now replace L in the first equation and solve for s:

5(18.5) + 6S = 175

92.5 + 6S = 175

Subtract 92.5 from both sides:

6S = 82.5

Divide both sides by 6:

S = 82.5 / 6 = 13.75

Large box = 18.5 kilograms

Small box = 13.75 kilograms