To determine the total amount Ben Frank charges, we need to break the problem down into two parts: the charge for the hours worked and the charge for the fixtures installed.
First, we need to calculate the cost for the hours Ben spent working.
- Ben worked for [tex]\( h = 7 \)[/tex] hours.
- He charges [tex]$15 per hour.
So, the cost for the hours worked is:
\[ 15 \text{ dollars/hour} \times 7 \text{ hours} = 105 \text{ dollars} \]
Next, we need to calculate the cost for the fixtures Ben installed.
- Ben installed \( f = 9 \) fixtures.
- He charges $[/tex]40 per fixture.
So, the cost for the fixtures installed is:
[tex]\[ 40 \text{ dollars/fixture} \times 9 \text{ fixtures} = 360 \text{ dollars} \][/tex]
Now, we add the cost of the hours worked and the cost of the fixtures installed to find the total charge.
[tex]\[ 105 \text{ dollars} + 360 \text{ dollars} = 465 \text{ dollars} \][/tex]
Hence, the total amount Ben Frank charges when he works 7 hours and installs 9 fixtures is [tex]\(\boxed{465}\)[/tex] dollars.
