To solve this problem, we need to set up an equation that represents the total distance Maria hiked using both the mountain trail and the canal trail.
Let's break down the given information:
- Maria hikes the mountain trail, which is 5 miles long.
- Let [tex]\(x\)[/tex] represent the number of times Maria hiked the mountain trail.
- [tex]\(x\)[/tex] times hiking the mountain trail results in a total distance of [tex]\(5x\)[/tex] miles.
- Maria also hikes the canal trail, which is 10 miles long.
- Let [tex]\(y\)[/tex] represent the number of times Maria hiked the canal trail.
- [tex]\(y\)[/tex] times hiking the canal trail results in a total distance of [tex]\(10y\)[/tex] miles.
Finally, we're told that the total distance Maria hiked is 90 miles. This means that the sum of the distances from hiking the mountain trail and the canal trail is 90 miles. Therefore, we can set up the following equation:
[tex]\[ 5x + 10y = 90 \][/tex]
This equation correctly represents the relationship between the number of times Maria hiked each trail and the total distance.
Let's look at each of the provided options:
1. [tex]\( x + y = 90 \)[/tex]
- This equation suggests that the number of hikes on both trails adds up to 90, which doesn't match the context of the problem since it doesn't account for the different distances.
2. [tex]\( 5x - 10y = 90 \)[/tex]
- This equation incorrectly subtracts the distances instead of adding them.
3. [tex]\( 90 - 10y = 5x \)[/tex]
- This equation can be rearranged to [tex]\( 5x + 10y = 90 \)[/tex], which actually matches our correct equation.
4. [tex]\( 90 + 10y = 5x \)[/tex]
- This equation suggests adding 90 to the distance hiked on the canal trail to equal the distance hiked on the mountain trail. This does not correctly represent the total distance hiked.
After evaluating each option, the correct equation to use is:
[tex]\[ 5x + 10y = 90 \][/tex]
So, the correct choice from the options provided is:
[tex]\[ 5x + 10y = 90 \][/tex]
