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. The forklift can carry upto either $45$ boxes or a weight of $2400$ pound. Which of the following systems of inequalities represents this relationship?

• A. $\{\begin{array}{c}40x+65y\le 2,400\\ x+y\le 45\end{array}$
• B. $\{\begin{array}{c}\frac{y}{40}+\frac{y}{65}\le 2,400\\ x+y\le 45\end{array}$
• C. $\{\begin{array}{c}40x+65y\le 45\\ x+y\le 2,400\end{array}$
• D. $\{\begin{array}{c}x+y\le 2,400\\ 40x+65y\le 2,400\end{array}$

Answer 1

The correct option is A $\{\begin{array}{c}40x+65y\le 2,400\\ x+y\le 45\end{array}$

Since $x$ is the number of $40$ pound boxes, $40x$ is total weight, in pounds, of the $40$ pound boxes; and since $y$ is the number of $65$ pound boxes, $65y$ is total weight, in pounds, of the $65$ pound boxes.

The combined weight of the boxes is therefore $40x+65y$, and the total number of boxes is $x+y$.

Since the forklift can carry up to $45$ boxes or up to $2,400$ pounds, the inequalities that represent these relationships are:

$40x+65y\le 2,400$ and $x+y\le 45$