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 4 large boxes and 8 small boxes has a total weight of 169 kilograms. A delivery of 2 large boxes and 3 small boxes has a total weight of 71 kilograms.

How much does each type of box weigh?

Weight of each large box:

Weight of each small box:

Answer 1

Let Large be notated by X

let small be notated by Y

by the first Sentence:

4X + 8Y = 169

by the second sentence:

2X + 3Y = 71

now to solve for the system of equations, solve for Y in one of the equations.

Y=(169-4X)/8

plug Y into the second equation.

2X + 3((169-4X)/8)=71

solve for x.

2X + 3(21.125-0.5X)=71

2X + 63.375-1.5X=71

.5X= 7.625

x= 15.25

this is the small box value.

now plug this value into any equation to solve for Y.

2(15.25) + 3Y =71

30.5+ 3Y = 71

3Y = 40.5

Y= 13.5

to check yourself, plug each number into each equation.

Answer 2

8sm=169kg; 169/8=21.125kg

2lg=71kg; 35.5kg