I own a large truck, and my neighbor owns four small trucks that are all identical. My truck can carry a load of at least 800 pounds more than each of her trucks, but no more than 1/3 of the total load her four trucks combined can carry. Based on these facts, what is the greatest load I can be sure that my large truck can carry, in pounds?

Guest Mar 1, 2020

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*I own a large truck, and my neighbor owns four small trucks that are all identical. My truck can carry a load of at least 800 pounds more than each of her trucks, but no more than 1/3 of the total load her four trucks combined can carry. Based on these facts, what is the greatest load I can be sure that my large truck can carry, in pounds?*

"no more than 1/3 of the total load" means it will carry 1/3 of the total load

Let A stand for how much your truck will carry.

Let B stand for how much one of your neighbor's trucks will carry.

A = B + 800

A = (1/3)(4B)

set the A's equal B + 800 = (1/3)(4B)

B + 800 = 4B/3

multiply both sides by 3 3B + 2,400 = 4B

subtract 3B from both sides 2,400 = B

Your truck will carry A = 2,400 + 800

Your truck will carry **A = 3,200**

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Guest Mar 2, 2020