Question

1. structure on a conveyor belt, there can only be two boxes moving at a time. the total weight of the boxes cannot be more than 300 pounds. let x and y represent the weights of two boxes on the conveyor belt.

a.
write an inequality that describes the weight limitation in terms of x and y.
b.
ly that describes the limit on the average weight a of the two boxes.
c.
two boxes are to be placed on the conveyor belt. the first box weighs 175 pounds. what is the maximum weight of the second box?

Explanation:

Step1: Write the inequality for total weight

The total weight of the two boxes is \(x + y\). Since it cannot be more than 300 pounds, the inequality is \(x + y\leq300\).

Step2: Find the inequality for average weight

The average weight \(a=\frac{x + y}{2}\). From \(x + y\leq300\), divide both sides by 2. We get \(a=\frac{x + y}{2}\leq\frac{300}{2}\), so \(a\leq150\).

Step3: Solve for the maximum weight of the second box

Let \(x = 175\) (weight of the first box). Substitute into \(x + y\leq300\). Then \(175+y\leq300\). Subtract 175 from both sides: \(y\leq300 - 175\), so \(y\leq125\).

Answer:

a. \(x + y\leq300\)
b. \(a\leq150\)
c. 125 pounds