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

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

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

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

Let's solve the problem to find how many miles, [tex]\( x \)[/tex], Debbie rode each evening.

1. Debbie rode 4 days, and each day she took two routes: a 12-mile ride in the morning and an unknown number of miles, [tex]\( x \)[/tex], in the evening.

2. By the end of the week (4 days), Debbie had ridden a total of 72 miles.

3. We need to set up an equation that represents the total number of miles she rode in a week. Each day, the total miles she rode was [tex]\( 12 + x \)[/tex].

4. Since she rode for 4 days, we multiply the daily mile total by 4:
[tex]\[
4 \times (12 + x) = 72
\][/tex]

5. Let's solve the equation for [tex]\( x \)[/tex]:

a. First, distribute the 4 to both terms inside the parentheses:
[tex]\[
4 \times 12 + 4 \times x = 72
\][/tex]
Which simplifies to:
[tex]\[
48 + 4x = 72
\][/tex]

b. Subtract 48 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
4x = 72 - 48
\][/tex]
[tex]\[
4x = 24
\][/tex]

c. Divide both sides by 4 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{24}{4}
\][/tex]
[tex]\[
x = 6
\][/tex]

Therefore, Debbie rode 6 miles each evening. The correct equation that helps us find the number of miles [tex]\( x \)[/tex] Debbie rode each evening is:

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