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 2 large boxes and 3 small boxes has a total weight of 78 kilograms. A delivery of 6 large boxes and 5 small boxes has a total weight of 180 kilograms. How much does each type of box weigh?

Answer 1

This is a system of equations problem. Two equations with two unknowns (L and S). Three ways to solve:

Graph, substitution, elimination.

Here are the equations, where L is wt.of lg. boxes; S is wt. of small boxes.

2L + 3S = 78; 6L + 5S = 180 Assuming you'd prefer not to graph the two lines (answer is where they'd cross), I'd suggest elimination, given the form of the equations.

We can eliminate the L variable if multiply 1st eqn by -3:

-6L + -9S = -234

6L + 5S = 180 Add them

0 - 4S = -54 so S = 13.5 kg. Substitute for S in 1st eqn.

2L + 3(13.5) = 78 → 2L + 40.5 = 78 → 2L = 37.5 → L = 18.75 kg.

Check in 2nd eqn: 6(18.75) + 5(13.5) = 112.5 + 67.5 = 180 kg.