Question
Wanting to save money, the next time Alex goes to a restaurant, his dinner and taxes combined comes to \( \$ 12.00 \). If taxes are equal to \( 13 \% \), what is the value of his dinner? Round to the nearest cent
Ask by Page Chandler. in Canada
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Alex's dinner costs \$10.62.
Solution
Let the cost of Alex's dinner be \( D \). Since the taxes are \( 13\% \) of the dinner cost, the tax amount is \( 0.13D \). The total cost, including dinner and taxes, is given by
\[
D + 0.13D = 12.
\]
Combining like terms, we have
\[
1.13D = 12.
\]
Now, solve for \( D \):
\[
D = \frac{12}{1.13} \approx 10.6195.
\]
Rounding to the nearest cent, the value of his dinner is \( \$10.62 \).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
To find the value of Alex's dinner before tax, we can use the following formula: Let \( D \) be the value of the dinner. The total bill, which is \( \$12.00 \), can be represented as: \[ D + 0.13D = 12.00 \] This simplifies to: \[ 1.13D = 12.00 \] Now, we divide both sides by \( 1.13 \): \[ D = \frac{12.00}{1.13} \approx 10.62 \] Rounding to the nearest cent, the value of Alex's dinner is approximately \( \$10.62 \).
