Debbie has been training for the Bayside Bike Race. The first week she trained, she rode 4 days and took the same two routes each day: 12 miles through her neighborhood in the morning and a shorter route on a park trail in the evening. By the end of the week, she had ridden a total of 72 miles.

Which equation can you use to find how many miles, [tex]x[/tex], Debbie rode each evening?

A. [tex]4(x + 12) = 72[/tex]

B. [tex]12x + 4 = 72[/tex]

C. [tex]12(x + 4) = 72[/tex]

D. [tex]4x + 12 = 72[/tex]

To find how many miles, [tex]\( x \)[/tex], Debbie rode each evening, let's break down the steps:

1. Understand the Problem:
- Debbie rode 4 days in a week.
- Each day, she rode 12 miles in the morning.
- By the end of the week, she rode a total of 72 miles.

2. Equation Setup:
- For each day, she rides a total distance of [tex]\( x + 12 \)[/tex] miles, where [tex]\( x \)[/tex] is the distance she rode each evening.
- Since she rode for 4 days, the total distance for those days can be represented as [tex]\( 4(x + 12) \)[/tex].

3. Equation:
- Set up the equation:
[tex]\[
4(x + 12) = 72
\][/tex]
- This equation represents the total distance Debbie rode over the week.

4. Solve for [tex]\( x \)[/tex]:
- Simplifying the equation gives:
[tex]\[
4(x + 12) = 72
\][/tex]
- Divide both sides by 4 to isolate the expression within the brackets:
[tex]\[
x + 12 = 18
\][/tex]
- Subtract 12 from both sides to solve for [tex]\( x \)[/tex]:
[tex]\[
x = 18 - 12
\][/tex]
[tex]\[
x = 6
\][/tex]

Therefore, Debbie rode 6 miles each evening. The correct equation from the options provided is [tex]\( 4(x + 12) = 72 \)[/tex].