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Answer :
Let’s break the problem into two parts.
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1. Wage for a Regular 40-Hour Week
Mr. Jones earns a basic rate of \[tex]$115 per hour. In a regular week, he works 40 hours. Therefore, his wage for a regular week is calculated as:
$[/tex][tex]$
\text{Regular Wage} = 115 \times 40 = 4600.
$[/tex][tex]$
So, his wage for a 40-hour week is \$[/tex]4600.
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2. Calculating the Overtime Hours
In another week, Mr. Jones’s total wage included an extra \[tex]$960, which resulted solely from overtime work. Overtime pay is at double time, meaning he earns:
$[/tex][tex]$
\text{Overtime Rate} = 2 \times 115 = 230 \text{ dollars per hour}.
$[/tex][tex]$
To find the number of overtime hours he worked, divide the extra wage by the overtime rate:
$[/tex][tex]$
\text{Overtime Hours} = \frac{960}{230} \approx 4.1739.
$[/tex][tex]$
Thus, Mr. Jones worked approximately $[/tex]4.1739[tex]$ overtime hours.
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In summary:
- His wage for a regular 40-hour week is \$[/tex]4600.
- He worked about [tex]$4.1739$[/tex] hours of overtime, given that overtime is paid at a rate of \[tex]$230 per hour.
- Combining both, his total wage for that week would be \$[/tex]4600 + \[tex]$960 = \$[/tex]5560.
--------------------------------------------------
1. Wage for a Regular 40-Hour Week
Mr. Jones earns a basic rate of \[tex]$115 per hour. In a regular week, he works 40 hours. Therefore, his wage for a regular week is calculated as:
$[/tex][tex]$
\text{Regular Wage} = 115 \times 40 = 4600.
$[/tex][tex]$
So, his wage for a 40-hour week is \$[/tex]4600.
--------------------------------------------------
2. Calculating the Overtime Hours
In another week, Mr. Jones’s total wage included an extra \[tex]$960, which resulted solely from overtime work. Overtime pay is at double time, meaning he earns:
$[/tex][tex]$
\text{Overtime Rate} = 2 \times 115 = 230 \text{ dollars per hour}.
$[/tex][tex]$
To find the number of overtime hours he worked, divide the extra wage by the overtime rate:
$[/tex][tex]$
\text{Overtime Hours} = \frac{960}{230} \approx 4.1739.
$[/tex][tex]$
Thus, Mr. Jones worked approximately $[/tex]4.1739[tex]$ overtime hours.
--------------------------------------------------
In summary:
- His wage for a regular 40-hour week is \$[/tex]4600.
- He worked about [tex]$4.1739$[/tex] hours of overtime, given that overtime is paid at a rate of \[tex]$230 per hour.
- Combining both, his total wage for that week would be \$[/tex]4600 + \[tex]$960 = \$[/tex]5560.
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