Question

A worker uses a forklift to move boxes that weigh either 40 pounds or 65 pounds each. Let x be the number of 40-pound boxes and y be the number of 65-pound boxes. The forklift can carry up to either 45 boxes or a weight of 2,400 pounds. Which of the following systems of inequalities represents this relationship?

• A. $40x+65\le 2400;x+y\le 45$
• B. $\frac{x}{40}+\frac{y}{65}\le 2400;x+y\le 45$
• C. $40x+65\le 45;x+y\le 2400$
• D. $40x+65\le 2400;x+y\le 2400$

Answer 1

The correct option is A

$40x+65\le 2400;x+y\le 45$

The first constraint is on the weight of the boxes. The total weight of the boxes cannot exceed 2400. Since there are x 40 pound boxes and y 65 pound boxes, total weight is (40x + 65 y). So,
$40x+65y\le 2400$
The total number of boxes cannot exceed 45. Total number of boxes is (x + y). So,
$x+y\le 45$
Hence, A is the correct choice.