Question

A bookkeeper charges $50, plus $40 for every additional hour of work. What is the maximum number of hours that the bookkeeper can be hired for $500?
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11
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12
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9
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8

Answer 1

Let's break down the costs associated with hiring the bookkeeper:

1. The initial charge is $50.
2. Each additional hour costs $40.

Let's denote the number of additional hours as \( h \). The total cost for hiring the bookkeeper can be calculated using the formula:

\[
\text{Total cost} = 50 + 40h
\]

We know the maximum amount we can spend is $500. Therefore, we can set up the equation:

\[
50 + 40h \leq 500
\]

Now, we need to solve for \( h \):

1. Subtract the initial charge from both sides:

\[
40h \leq 500 - 50
\]

\[
40h \leq 450
\]

2. Divide both sides by 40:

\[
h \leq \frac{450}{40}
\]

\[
h \leq 11.25
\]

Since \( h \) represents the number of additional hours and must be a whole number, the maximum integer value for \( h \) is 11 hours.

Therefore, the total number of hours that the bookkeeper can be hired is:

\[
1 \text{ (initial hour)} + 11 \text{ (additional hours)} = 12 \text{ hours}
\]

Thus, the maximum number of hours that the bookkeeper can be hired for $500 is **12**.