A moving truck can tow a trailer if the combined weight of the trailer and the boxes it contains is

Question

A moving truck can tow a trailer if the combined weight of the trailer and the boxes it contains is no more than $4,600$ pounds. What is the maximum number of boxes this truck can tow in a trailer with a weight of $500$ pounds if each box weighs $120$ pounds?

A.

$34$

B.

$35$

C.

$38$

D.

$39$

Accepted Answer

Choice A is correct. It&rsquo;s given that the truck can tow a trailer if the combined weight of the trailer and the boxes it contains is no more than 4,600 pounds. If the trailer has a weight of 500 pounds and each box weighs 120 pounds, the expression 500 + 120 b , where b is the number of boxes, gives the combined weight of the trailer and the boxes. Since the combined weight must be no more than 4,600 pounds, the possible numbers of boxes the truck can tow are given by the inequality 500 + 120 b d 4,600 . Subtracting 500 from both sides of this inequality yields 120 b d 4,100 . Dividing both sides of this inequality by 120 yields b d 205 6 , or b is less than or equal to approximately 34.17 . Since the number of boxes, b , must be a whole number, the maximum number of boxes the truck can tow is the greatest whole number less than 34.17 , which is 34 . Choice B is incorrect. Towing the trailer and 35 boxes would yield a combined weight of 4,700 pounds, which is greater than 4,600 pounds. Choice C is incorrect. Towing the trailer and 38 boxes would yield a combined weight of 5,060 pounds, which is greater than 4,600 pounds. Choice D is incorrect. Towing the trailer and 39 boxes would yield a combined weight of 5,180 pounds, which is greater than 4,600 pounds.

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