Question

This is not a quiz!please hurry and answer this question because I have a assignment I need to do and this will help me for notes!Question: A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 3 large boxes and 5 small boxes has a total weight of 75 kilograms. A delivery of 9 large boxes and 7 small boxes has a total weight of 171 kilograms. How much does each type of box weigh?

Answer 1

weight of each large box is 13.75kg and weight of each small box is 6.75 kg

Step-by-step explanation:

let the number of large boxes = x

let the number of small boxes = y

A delivery of 3 large boxes and 5 small boxes has a total weight of 75 kilograms:

3x + 5y = 75 ...equation 1

A delivery of 9 large boxes and 7 small boxes has a total weight of 171 kilograms:

9x + 7y = 171 ...equation 2

Using elimination method:

We would be eliminating x by ensuring both equations have same coefficient of x

Multiply equation 1 by 3:

9x + 15y = 225 ...equation 1

9x + 7y = 171 ...equation 2

subtract equation 2 from 1:

9x - 9x + 15y - 7y = 225 - 171

8y = 54

8y/8 = 54/8

y = 6.75

Substitute for y in any of the equation:

using 9x + 7y = 171 ...equation 2

9x + 7(6.75) = 171

9x + 47.25 = 171

9x = 171 - 47.25

9x = 123.75

x = 123.75/9

x = 13.75

Hence, weight of each large box is 13.75kg and weight of each small box is 6.75 kg