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?

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pukwedgieamerica pukwedgieamerica · Answer 1 · 2020-08-20T14:55:19+02:00

Answer:

one large box equals 15.75kg

one small box equals 13.75kg

Step-by-step 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:

[tex]5l+3s=120\\7l+9s=234[/tex]

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

[tex]3(5l+3s=120)\\7l+9s=234\\\\15l+9s=360\\7l+9s=234[/tex]

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

[tex]15l+9s=360\\-(7l+9s=234)\\8l=126\\\frac{8l}{8}=\frac{126}{8}\\l=15.75[/tex]

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

[tex]5l+3s=120\\5(15.75)+3s=120\\78.75+3s=120\\78.85-78.75+3s=120-78.75\\3s=41.25\\\frac{3s}{3}=\frac{41.25}{3}\\s=13.75[/tex]

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