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Chapter 5: Problem 40

Nadia works exactly 40 hours each week and earns a minimum of 1,200 dollar every 4 weeks. Her hourly rate of pay is determined by the job she is assigned and may vary. If x is Nadia's average hourly pay for a 4 -week period, which of the following inequalities best describes x ? F. \(x \leq 7.50\) G. \(x \geq \) H. \(x \geq \) 30.00 J. \(x \geq \)30.00 K. \(x \geq \) 120.00

Short Answer

Expert verified
Answer: G. \(x \geq 7.50\)

Step by step solution

01

Calculate the total hours worked in 4 weeks

First, let's find out how many hours Nadia works during the 4 weeks. Since she works 40 hours each week, we need to multiply this by 4. Total hours worked = (hours per week) × (number of weeks) Total hours worked = 40 × 4 Total hours worked = 160 So Nadia works 160 hours during the 4-week period.
02

Calculate Nadia's minimum earning by dividing her total earnings.

We know that Nadia earns at least 1,200 dollars in 4 weeks. Now, we need to find her minimum average hourly pay by dividing her total earnings by the total hours worked. Minimum average hourly pay (x) = (total earnings) / (total hours worked) x = 1200 / 160 x = 7.50
03

Express the inequality

Since Nadia earns at least 1,200 dollars in 4 weeks, her average hourly pay (x) should be greater than or equal to 7.50 dollars. Therefore, the correct inequality is: x ≥ 7.50 From the given options, this corresponds to option: G. \(x \geq 7.50\)

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