Question

A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 5 large boxes and 3 small boxes has a total weight of 120 kilograms. A delivery of 7 large boxes and 9 small boxes has a total weight of 234 kilograms. How much does each type of box weigh?

Answer 1

one large box equals 15.75kg

one small box equals 13.75kg

Explanation:

First, identify your variables:

Let "l" represent the weight of one large box.

Let"s" represent the weight of one small box.

Then, stack the two equations on top of each other:

`5l+3s=120\\7l+9s=234`

Next, multiply the first equation by 3 so we can use elimination of the "s" variable to find the "l" variable first:

`3(5l+3s=120)\\7l+9s=234\\\\15l+9s=360\\7l+9s=234`

Now, subtract the two equations to cancel out the s-variable and find the l-variable:

`15l+9s=360\\-(7l+9s=234)\\8l=126\\(8l)/(8)=(126)/(8)\\l=15.75`

Then, substitute your l-variable in the original first equation to find the s-variable:

`5l+3s=120\\5(15.75)+3s=120\\78.75+3s=120\\78.85-78.75+3s=120-78.75\\3s=41.25\\(3s)/(3)=(41.25)/(3)\\s=13.75`

With all the information that is collected, you find that one large box weighs 15.75kg and one small box weighs 13.75kg.