Question
A plumber charges $30, plus $15 for every additional hour of work. What is the maximum number of hours that the plumber can be hired for $160?
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8
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6
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7
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5
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8
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6
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7
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5
Answers
GPT-4o mini
To determine the maximum number of hours the plumber can be hired for $160, we can set up the problem using the plumber's pricing structure.
The total cost can be represented by the equation:
\[
\text{Total Cost} = 30 + 15h
\]
where \( h \) is the number of additional hours worked.
We want to find \( h \) when the total cost is $160:
\[
160 = 30 + 15h
\]
Now, we'll solve for \( h \):
1. Subtract 30 from both sides:
\[
160 - 30 = 15h
\]
\[
130 = 15h
\]
2. Now, divide both sides by 15:
\[
h = \frac{130}{15}
\]
\[
h \approx 8.67
\]
Since \( h \) represents the number of additional hours, we need to round down to the nearest whole number since the plumber can't work for a fraction of an hour. Thus, the maximum additional hours \( h \) can be 8.
Now we add the initial hour (the base price):
\[
\text{Total hours} = 1 + h = 1 + 8 = 9 \text{ hours}
\]
However, by employing the number of hours (assuming maximum under the constraints of the cost), we find:
For an actual answer corresponding to the choices provided:
If \( h = 8 \), total cost is:
\[
30 + 15 \times 8 = 30 + 120 = 150
\]
If \( h = 7 \):
\[
30 + 15 \times 7 = 30 + 105 = 135
\]
If \( h = 6 \):
\[
30 + 15 \times 6 = 30 + 90 = 120
\]
If \( h = 5 \):
\[
30 + 15 \times 5 = 30 + 75 = 105
\]
The closest budget near $160 in hours allocated is:
Only additional \( 8 \) hours is permissible if nearing \( 150\).
Thus maximum obtainable hours under budget \(= 8.67 \).
However, fitting into the choices provided:
The maximum number of hours that can be effectively charged within $160 total for work would be:
**Answer: 8 (including base hour). Unfortunately, this is not listed in available options hence assuming choices meant 1 additional hour maximum – thus max is constrained to be 7 adjusted or considered 6 considerably maximum possible as remotely available.**
The total cost can be represented by the equation:
\[
\text{Total Cost} = 30 + 15h
\]
where \( h \) is the number of additional hours worked.
We want to find \( h \) when the total cost is $160:
\[
160 = 30 + 15h
\]
Now, we'll solve for \( h \):
1. Subtract 30 from both sides:
\[
160 - 30 = 15h
\]
\[
130 = 15h
\]
2. Now, divide both sides by 15:
\[
h = \frac{130}{15}
\]
\[
h \approx 8.67
\]
Since \( h \) represents the number of additional hours, we need to round down to the nearest whole number since the plumber can't work for a fraction of an hour. Thus, the maximum additional hours \( h \) can be 8.
Now we add the initial hour (the base price):
\[
\text{Total hours} = 1 + h = 1 + 8 = 9 \text{ hours}
\]
However, by employing the number of hours (assuming maximum under the constraints of the cost), we find:
For an actual answer corresponding to the choices provided:
If \( h = 8 \), total cost is:
\[
30 + 15 \times 8 = 30 + 120 = 150
\]
If \( h = 7 \):
\[
30 + 15 \times 7 = 30 + 105 = 135
\]
If \( h = 6 \):
\[
30 + 15 \times 6 = 30 + 90 = 120
\]
If \( h = 5 \):
\[
30 + 15 \times 5 = 30 + 75 = 105
\]
The closest budget near $160 in hours allocated is:
Only additional \( 8 \) hours is permissible if nearing \( 150\).
Thus maximum obtainable hours under budget \(= 8.67 \).
However, fitting into the choices provided:
The maximum number of hours that can be effectively charged within $160 total for work would be:
**Answer: 8 (including base hour). Unfortunately, this is not listed in available options hence assuming choices meant 1 additional hour maximum – thus max is constrained to be 7 adjusted or considered 6 considerably maximum possible as remotely available.**