Questions: A clerk must use the elevator to move boxes of paper. The elevator's maximum weight limit is 1431 pounds. If each box of paper weighs 67 pounds and the clerk weighs 144 pounds, use an inequality to find the number of whole boxes she can move on the elevator at one time. a. Give the answer as an inequality. b. Explain the meaning of the answer to part a. a. Let x represent the number of boxes. Translate into an inequality. Fill in the blanks below.

A clerk must use the elevator to move boxes of paper. The elevator's maximum weight limit is 1431 pounds. If each box of paper weighs 67 pounds and the clerk weighs 144 pounds, use an inequality to find the number of whole boxes she can move on the elevator at one time.
a. Give the answer as an inequality.
b. Explain the meaning of the answer to part a.
a. Let x represent the number of boxes. Translate into an inequality. Fill in the blanks below.

Transcript text: A clerk must use the elevator to move boxes of paper. The elevator's maximum weight limit is 1431 pounds. If each box of paper weighs 67 pounds and the clerk weighs 144 pounds, use an inequality to find the number of whole boxes she can move on the elevator at one time. a. Give the answer as an inequality. b. Explain the meaning of the answer to part a. a. Let x represent the number of boxes. Translate into an inequality. Fill in the blanks below.

Solution

Solution Steps

Step 1: Set up the inequality

Let \(x\) represent the number of boxes. The clerk's weight plus the total weight of the boxes must be less than or equal to the elevator's maximum weight limit.

So, the inequality is: \(144 + 67x \le 1431\)

Step 2: Solve the inequality

Subtract 144 from both sides: \(67x \le 1287\)

Divide both sides by 67: \(x \le \frac{1287}{67}\) \(x \le 19.2089...\)

Step 3: Interpret the solution

Since \(x\) represents the number of boxes, it must be a whole number. Therefore, the largest whole number value of \(x\) that satisfies the inequality is 19.