Let's analyze the information provided and solve the problem step-by-step.
1. Understand the Information Given:
- Matt paid a total amount of \[tex]$50 at a restaurant.
- This total amount includes a 10% tip.
2. Define the Problem:
- We need to find out what the original check amount (before the tip) was.
3. Break Down the Percentages:
- The total amount Matt paid is the sum of the original check amount and the 10% tip on that amount.
4. Set Up the Equation:
- Let the original check amount before the tip be \( x \).
- The tip given is 10% of \( x \), which can be written as \( 0.10 \times x \).
- Therefore, the total paid amount is the original check amount plus the tip:
\[
x + 0.10x = 50
\]
5. Simplify the Equation:
- Combine like terms:
\[
1.10x = 50
\]
6. Solve for \( x \):
- Divide both sides by 1.10 to isolate \( x \):
\[
x = \frac{50}{1.10}
\]
7. Calculate \( x \):
- Performing the division, we find:
\[
x \approx 45.45454545454545
\]
8. Identify the Most Appropriate Answer:
- From the given options, the value closest to this calculated amount is \$[/tex]45, which corresponds to option C.
Thus, the correct answer is:
C. \$45
