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?
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.
+36916 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
