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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
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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 

.

 Mar 2, 2020

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