Certainly! Let's break down the problem step-by-step to find the correct equation representing the number of times Maria hiked each trail.
1. Understanding the Variables and Total Miles:
- Maria hiked a total of 90 miles.
- There are two types of trails:
- A 5-mile mountain trail.
- A 10-mile canal trail.
2. Introducing Variables:
- Let [tex]\( x \)[/tex] represent the number of times Maria hiked the 5-mile mountain trail.
- Let [tex]\( y \)[/tex] represent the number of times Maria hiked the 10-mile canal trail.
3. Formulating the Problem:
- The total distance hiked on the mountain trail would be [tex]\( 5x \)[/tex] miles since each hike on this trail covers 5 miles.
- The total distance hiked on the canal trail would be [tex]\( 10y \)[/tex] miles since each hike on this trail covers 10 miles.
4. Setting Up the Equation:
- The sum of these distances should equal the total distance hiked, which is 90 miles. Hence, the equation representing this relationship would be:
[tex]\[
5x + 10y = 90
\][/tex]
5. Rearranging the Equation:
- We can rearrange this equation to isolate one of the variables if necessary. For instance, solving for [tex]\( 5x \)[/tex] in terms of [tex]\( y \)[/tex]:
[tex]\[
5x = 90 - 10y
\][/tex]
This gives us the equation:
[tex]\[
90 - 10y = 5x
\][/tex]
Therefore, the correct equation to use in order to find the number of times Maria hiked each trail is:
[tex]\[
90 - 10y = 5x
\][/tex]
So, among the given choices, the correct equation is:
[tex]\[
90 - 10y = 5x
\][/tex]
Thus, the third option is the correct one.
