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# Inequality

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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 $$\frac{1}{5}$$ 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?

Jan 19, 2022

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I'm pretty sure this question is impossible. We can say t=800+x where t is your truck and x is her trucks and then write t<=(1/5)(4x) which is also t<=4x/5. Let's assume t=4x/5. Then if we solve the equation we get x=-4000 which is clearly not possible since the truck shouldn't carry a negative weight. Also, if t=4x/5 -1, we subtract 1 to put an equal sign instead of a < sign, then we get x=-4005 and x is decreasing in value(since it is negative) and so we can never get a positive answer. This means the problem shouldn't be possible.

Jan 19, 2022
#2
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Based on looking at other problems similar to this, I think you meant 1/3 of the total load which means if we say t=800+x and t=4/3x then subtract the first equation from the second, we get 1/3x=800, or x=2400. Then to solve for t we add 800 to get t=3200.

So the greatest load the truck can carry is 3200 pounds.

ImDecentAtMath  Jan 20, 2022