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, $ x $, Debbie rode each evening?

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

To find how many miles Debbie rode each evening, the equation is 48 + 4x = 72, where 48 represents the total miles from the morning rides and x is the miles ridden each evening.

Explanation:

determine how many miles, x, Debbie rode each evening when she had trained a total of 72 miles by the end of the week, riding 4 days, taking two routes each day, with one route being 12 miles. To solve this, let's identify the components we know: the total miles ridden (72 miles), the miles ridden in the neighborhood each morning (12 miles), and the number of days she rode (4 days). We need to find the evening route's miles, x.

Debbie rode 12 miles in the morning and x miles in the evening each of the 4 days. So for 4 days, the morning rides total 48 miles (12 miles/day × 4 days). The total distance ridden is the sum of the morning rides and the evening rides over the 4 days. The equation representing this scenario would be:

48 + 4x = 72

This equation indicates that the total miles Debbie rode in the mornings plus four times the miles she rode each evening equals 72 miles, the total distance she rode by the end of the week.