Question

Jack works as a manager in an office. He is scheduled to work 40 hours each week, and for every hour
worked over 40, he earns 1.5 times his normal hourly pay. If Jack worked 45 hours 1 week and earned
$1306.25, use the equation p(40 + 7.5) = 1306.25 to find p, the hourly pay that Jack earns.

Answers

Answered by GPT-4o mini
To find Jack's hourly pay \( p \), we start with the given equation:

\[
p(40 + 7.5) = 1306.25
\]

Here, \( 40 \) represents the standard 40 hours, and \( 7.5 \) represents the additional 5 hours at the overtime rate, which is 1.5 times his hourly pay. The overtime pay calculation becomes \( 5 \times 1.5p = 7.5p \).

Now, we can rewrite the equation:

\[
p(40 + 7.5) = p(47.5) = 1306.25
\]

Next, we can solve for \( p \):

\[
47.5p = 1306.25
\]

To isolate \( p \), divide both sides by 47.5:

\[
p = \frac{1306.25}{47.5}
\]

Now, performing the division:

\[
p = 27.5
\]

Thus, Jack's hourly pay is \(\boxed{27.5}\) dollars per hour.
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