To determine the equation that can be used to find [tex]\( h \)[/tex], the number of hours Lindsay worked last week, let's follow the steps closely and derive the appropriate equations.
### Step-by-Step Solution
1. Identifying components:
- Hourly rate: [tex]\( \$10 \)[/tex] per hour.
- Bonus: [tex]\( \$60 \)[/tex].
- Fraction of paycheck spent on dinner with bonus: [tex]\( \frac{1}{15} \)[/tex].
- Fraction of paycheck spent on dinner without bonus: [tex]\( \frac{1}{10} \)[/tex].
2. Expression for paycheck with bonus:
- Total earnings with bonus for [tex]\( h \)[/tex] hours: [tex]\[ 10h + 60 \][/tex]
3. Expression for spending on dinner with bonus:
- Fraction spent on dinner with bonus: [tex]\[ \frac{1}{15}(10h + 60) \][/tex]
4. Expression for paycheck without bonus:
- Total earnings without bonus for [tex]\( h \)[/tex] hours: [tex]\[ 10h \][/tex]
5. Expression for spending on dinner without bonus:
- Fraction spent on dinner without bonus: [tex]\[ \frac{1}{10}(10h) \][/tex]
6. Setting up the equation:
Lindsay spends the same amount of money on dinner whether or not she receives the bonus. Therefore, we set the amount spent on dinner with the bonus equal to the amount spent on dinner without the bonus:
[tex]\[
\frac{1}{15}(10h + 60) = \frac{1}{10}(10h)
\][/tex]
### Conclusion
The equation that can be used to find [tex]\( h \)[/tex], the number of hours Lindsay worked last week, is:
[tex]\[
\frac{1}{15}(10h + 60) = \frac{1}{10}(10h)
\][/tex]
Hence, the correct choice is:
[tex]\[
\boxed{\frac{1}{15}(10h + 60) = \frac{1}{10}(10h)}
\][/tex]
