Pregunta
3. The accountant charged \( \$ 35 \) for the first hour of work and \( \$ 23 \) for each hour after that. He earned a total of \( \$ 127 \). How many hours did he work?
Ask by Lawson Johnston. in the United States
Mar 13,2025
Solución de inteligencia artificial de Upstudy
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The accountant worked 5 hours.
Solución
Let \( h \) be the total number of hours worked.
1. The accountant charged \( \$35 \) for the first hour and \( \$23 \) for each additional hour. Thus, the total charge can be written as:
\[
35 + 23 \cdot (h - 1) = 127
\]
2. Subtract \( 35 \) from both sides:
\[
23 \cdot (h - 1) = 127 - 35 = 92
\]
3. Divide both sides by \( 23 \):
\[
h - 1 = \frac{92}{23} = 4
\]
4. Add \( 1 \) to both sides to solve for \( h \):
\[
h = 4 + 1 = 5
\]
Thus, the accountant worked \( 5 \) hours.
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Simplifique esta solución Extra Insights
To determine how many hours the accountant worked, we start with the total earned, which is \( \$ 127 \). He charged \( \$ 35 \) for the first hour, leaving \( 127 - 35 = 92 \) dollars for the subsequent hours. Since he charges \( \$ 23 \) for each of those hours, we set up the equation \( 23x = 92 \) to solve for \( x \). When we divide \( 92 \) by \( 23 \), we find that \( x = 4 \). This means he worked 4 hours after the first hour. Adding the first hour to this, the total number of hours worked is \( 4 + 1 = 5 \) hours. So, the accountant worked a total of **5 hours**.
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