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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?

 Mar 1, 2020
 #1
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Let x be the weight the large truck can carry, and let y be the weight that the small truck can carry.  Then x >= y + 800 and x <= 1/3*4*(4y) = 16/3*y.  We can solve these inequalities to get x <= 12800/13 and y <= 2400/13, so the maximum weight for the large truck is 12800/13.

 Mar 1, 2020
 #2
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x = small truck capacity

 

x+800 = your truck

 

 

x+800 >=  4   * 1/3 x

800 >= 4/3 x

x <= 2400

 

then big truck    x+800 <=    3200  lbs

 Mar 1, 2020

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