Solving a value mixture problem using a system of linear equations

Question

A delivery truck is transporting boxes of two sizes: large and small. The combined weight of a large box and a small box is 75 pounds. The truck is transporting 55 large boxes and 60 small boxes. If the truck is carrying a total of 4300 pounds in boxes, how much does each type of box weigh?

Answer 1

L+S = 75

55L + 60S = 4300, multiply 1st equation by 55 and subtract from 2nd equation to get

55L + 55S = 55(75)

5S = 4300-55(75)

S = 860-825 =35 pounds for the smaller box

L = 75-35 = 40 pounds for the larger box

55(40) + 60(35) = 2200 + 2100= 4300 pounds total

35+40 = 75 pounds for one of each box together