Solving a word problem using a system of linear equations of the form Ax + By = C

Question

A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 9 large boxes and 7 small boxes has a total weight of 171 kilograms. A delivery of 3 large boxes and 5 small boxes has a total weight of 75 kilograms.

How much does each type of box weigh?

Answer 1

9L + 7S = 171

3L + 5S = 75

multiply the 2nd by 3 to get

9L + 15S = 225 then subtract the 1st equation to get

8S = 54

S = 54/8 = 27/4 = 6 3/4 kg

3L = 75-5(27/4) = 41 1/4

L = 41 1/4 /3 = 13 3/4 kg