Let's denote the number of hours Lindsay worked last week as [tex]\( h \)[/tex].
Step-by-step solution:
1. Calculate Lindsay's Total Earnings:
- Lindsay earns [tex]$10 per hour and worked for \( h \) hours
- Therefore, her earnings from working \( h \) hours is \( 10h \) dollars.
- She also receives a $[/tex]60 bonus for her good job performance.
- Thus, her total earnings are:
[tex]\[
10h + 60
\][/tex]
2. Calculate the Amount Spent on Dinner with Bonus:
- She spends [tex]\(\frac{1}{15}\)[/tex] of her paycheck on dinner.
- Her paycheck with the bonus is [tex]\( 10h + 60 \)[/tex] dollars.
- Hence, the amount she spends on dinner is:
[tex]\[
\frac{1}{15}(10h + 60)
\][/tex]
3. Calculate the Amount Spent on Dinner without Bonus:
- Without the $60 bonus, her earnings would just be [tex]\( 10h \)[/tex] dollars.
- She would spend [tex]\(\frac{1}{10}\)[/tex] of this amount on dinner.
- Hence, the amount she spends on dinner without the bonus is:
[tex]\[
\frac{1}{10}(10h)
\][/tex]
4. Set Up the Equation:
- According to the problem, we know these two amounts should be equal for the chosen number of hours [tex]\( h \)[/tex]:
[tex]\[
\frac{1}{15}(10h + 60) = \frac{1}{10}(10h)
\][/tex]
Therefore, the correct equation to find [tex]\( h \)[/tex] is:
[tex]\[
\frac{1}{15}(10 h + 60) = \frac{1}{10}(10 h)
\][/tex]
This matches the first option provided in the multiple-choice answers.
So, the correct equation is:
[tex]\[
\frac{1}{15}(10 h + 60) = \frac{1}{10}(10 h).
\][/tex]
