Question

tion 1
part a: which inequality represents
the situation, where x represents the
number of new workers sandra can
hire?
a) $200 \geq 120 + 16x \leq 325$
b) $200 \leq 120 + 16x \leq 325$
c) $200 \geq 120 + 16x < 325$
d) $200 \leq 120 + 16x > 325$
part b: what is the largest number of
workers sandra can hire? ____________

Explanation:

Part A

Step1: Analyze the inequality structure

We need to find an inequality where \(120 + 16x\) (total cost with new workers) is between 200 and 325 (inclusive or not). The total cost should be at least 200 and at most 325, so the correct form is \(200\leq120 + 16x\leq325\). Option a has wrong direction for the left inequality, option c has wrong left and right, option d has wrong right inequality.

Step2: Confirm the correct option

From the analysis, option b (\(200\leq120 + 16x\leq325\)) is correct.

Step1: Solve the inequality \(200\leq120 + 16x\leq325\)

First, subtract 120 from all parts: \(200 - 120\leq120 + 16x- 120\leq325 - 120\), which simplifies to \(80\leq16x\leq205\).

Step2: Divide by 16

Divide each part by 16: \(\frac{80}{16}\leq\frac{16x}{16}\leq\frac{205}{16}\), so \(5\leq x\leq12.8125\). Since \(x\) is the number of workers (integer), the largest integer \(x\) is 12.

Answer:

b) \(200\leq120 + 16x\leq325\)

Part B