Answer :
We are given that Mr. Jones earns a basic wage of \[tex]$8.5 per hour for a 40‑hour week, and any overtime is paid at double time. This means the overtime rate is
$[/tex][tex]$
\text{overtime rate} = 2 \times 8.5 = 17 \text{ dollars per hour}.
$[/tex][tex]$
We will solve the two parts step by step.
─────────────────────────────
Part (1): If Mr. Jones worked 2 hours of overtime during a particular week, what was his total pay for that week?
1. The pay for the regular 40 hours is
$[/tex][tex]$
\text{regular pay} = 40 \times 8.5 = 340 \text{ dollars}.
$[/tex][tex]$
2. The overtime pay for 2 hours at \$[/tex]17 per hour is
[tex]$$
\text{overtime pay} = 2 \times 17 = 34 \text{ dollars}.
$$[/tex]
3. Thus, the total pay for the week is
[tex]$$
\text{total pay} = 340 + 34 = 374 \text{ dollars}.
$$[/tex]
─────────────────────────────
Part (2): If Mr. Jones’s wage for another week was \[tex]$960 and overtime is paid at double time, how many overtime hours did he work?
1. We already know his regular pay for 40 hours is
$[/tex][tex]$
\text{regular pay} = 340 \text{ dollars}.
$[/tex][tex]$
2. Let $[/tex]x[tex]$ be the number of overtime hours worked. His overtime pay will then be
$[/tex][tex]$
\text{overtime pay} = 17x \text{ dollars}.
$[/tex][tex]$
3. The total wage for the week is given by
$[/tex][tex]$
340 + 17x = 960.
$[/tex][tex]$
4. Subtract 340 from both sides to solve for $[/tex]x[tex]$:
$[/tex][tex]$
17x = 960 - 340 = 620.
$[/tex][tex]$
5. Now, divide both sides by 17:
$[/tex][tex]$
x = \frac{620}{17} \approx 36.470588235294116.
$[/tex][tex]$
─────────────────────────────
Summary of the Answers:
- For the week with 2 overtime hours:
- Regular pay: \$[/tex]340
- Overtime pay: \[tex]$34
- Total pay: \$[/tex]374
- For the week with a total wage of \[tex]$960, the number of overtime hours worked is approximately
$[/tex][tex]$
36.470588235294116 \text{ hours}.
$[/tex]$
$[/tex][tex]$
\text{overtime rate} = 2 \times 8.5 = 17 \text{ dollars per hour}.
$[/tex][tex]$
We will solve the two parts step by step.
─────────────────────────────
Part (1): If Mr. Jones worked 2 hours of overtime during a particular week, what was his total pay for that week?
1. The pay for the regular 40 hours is
$[/tex][tex]$
\text{regular pay} = 40 \times 8.5 = 340 \text{ dollars}.
$[/tex][tex]$
2. The overtime pay for 2 hours at \$[/tex]17 per hour is
[tex]$$
\text{overtime pay} = 2 \times 17 = 34 \text{ dollars}.
$$[/tex]
3. Thus, the total pay for the week is
[tex]$$
\text{total pay} = 340 + 34 = 374 \text{ dollars}.
$$[/tex]
─────────────────────────────
Part (2): If Mr. Jones’s wage for another week was \[tex]$960 and overtime is paid at double time, how many overtime hours did he work?
1. We already know his regular pay for 40 hours is
$[/tex][tex]$
\text{regular pay} = 340 \text{ dollars}.
$[/tex][tex]$
2. Let $[/tex]x[tex]$ be the number of overtime hours worked. His overtime pay will then be
$[/tex][tex]$
\text{overtime pay} = 17x \text{ dollars}.
$[/tex][tex]$
3. The total wage for the week is given by
$[/tex][tex]$
340 + 17x = 960.
$[/tex][tex]$
4. Subtract 340 from both sides to solve for $[/tex]x[tex]$:
$[/tex][tex]$
17x = 960 - 340 = 620.
$[/tex][tex]$
5. Now, divide both sides by 17:
$[/tex][tex]$
x = \frac{620}{17} \approx 36.470588235294116.
$[/tex][tex]$
─────────────────────────────
Summary of the Answers:
- For the week with 2 overtime hours:
- Regular pay: \$[/tex]340
- Overtime pay: \[tex]$34
- Total pay: \$[/tex]374
- For the week with a total wage of \[tex]$960, the number of overtime hours worked is approximately
$[/tex][tex]$
36.470588235294116 \text{ hours}.
$[/tex]$
