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 solve this problem, we need to determine how many miles Debbie rode each evening during her training week. Let's break down the information given:

1. Debbie trained for 4 days during the week.
2. Each day, she rode 12 miles in the morning.
3. She also rode an additional "x" miles in the evening, which we need to find.
4. By the end of the week, she had ridden a total of 72 miles.

Now, let's set up an equation to represent the total distance she rode:

- Each day, Debbie rides a total of [tex]$ (12 + x) $[/tex] miles: 12 miles in the morning and "x" miles in the evening.
- Over 4 days, the total distance ridden can be expressed as [tex]$ 4 \times (12 + x) $[/tex].

According to the problem, the total distance over the week is 72 miles. So, we can set up the equation:

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

Let's solve this equation step by step to find the value of [tex]$ x $[/tex]:

1. Distribute the 4:
[tex]$ 4 \times 12 + 4 \times x = 72 $[/tex]
This simplifies to:
[tex]$ 48 + 4x = 72 $[/tex]

2. Subtract 48 from both sides to isolate the term with [tex]$ x $[/tex]:
[tex]$ 4x = 72 - 48 $[/tex]
[tex]$ 4x = 24 $[/tex]

3. 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 equation we used to find this was:

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

So, the correct equation from the options given is [tex]$ 4(x + 12) = 72 $[/tex], and the number of miles Debbie rode each evening is 6.