note: please make sure to properly format your answers. all dollar figures in the answers need to include…

note: please make sure to properly format your answers. all dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma ($2,354.67). all percentage values in the answers need to include a percentage sign (%). for all items without specific rounding instructions, round your answers to two decimal places, show both decimal places (5.06).\nmichael earns $21 per hour and works 40 hours per week. how many overtime hours would he have to work in a week for his time - and - a - half overtime pay to be greater than his regular gross pay?

note: please make sure to properly format your answers. all dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma ($2,354.67). all percentage values in the answers need to include a percentage sign (%). for all items without specific rounding instructions, round your answers to two decimal places, show both decimal places (5.06).\nmichael earns $21 per hour and works 40 hours per week. how many overtime hours would he have to work in a week for his time - and - a - half overtime pay to be greater than his regular gross pay?

Answer

Explanation:

Step1: Calculate regular - gross pay

Regular - gross pay (=\text{Hourly rate}\times\text{Regular hours}). Given hourly rate (r = 21) dollars per hour and regular hours (h_{r}=40) hours. So, regular - gross pay (P_{r}=21\times40 = 840) dollars.

Step2: Calculate overtime pay formula

Overtime pay rate is time - and - a - half. So, overtime pay rate (r_{o}=21\times1.5=31.5) dollars per hour. Let the number of overtime hours be (x). Then overtime pay (P_{o}=31.5x).

Step3: Set up the inequality

We want (P_{o}>P_{r}). Substitute the expressions for (P_{o}) and (P_{r}): (31.5x>840).

Step4: Solve the inequality for (x)

Divide both sides of the inequality (31.5x>840) by (31.5). (x>\frac{840}{31.5}). (\frac{840}{31.5}=\frac{8400}{315}=\frac{160}{6}\approx26.67). Since the number of hours is a non - negative real number and we are talking about whole hours (in a practical work - hour context), and (x>26.67), the smallest whole number (x) for which the inequality holds is (x = 27).

Answer:

(27)