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Sagot :
Sure, let's find the correct equation that can be used to determine the number of times Maria hiked each of the two trails.
### Step-by-Step Solution:
1. Identify the 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.
2. Set Up the Equation:
Maria hiked a total of 90 miles combining both trails. For each hiking trip:
- Each time Maria hikes the mountain trail, she covers 5 miles.
- Each time Maria hikes the canal trail, she covers 10 miles.
Therefore, the total distance covered when hiking both trails can be expressed as:
[tex]\[ 5x + 10y = 90 \][/tex]
3. Simplify the Equation:
We can simplify the equation by organizing it in different forms. One way to clearly express [tex]\( x \)[/tex] in terms of [tex]\( y \)[/tex] could be rearranging the given equation.
Let's look at the choices and find their equivalence:
- Option 1: [tex]\( x + y = 90 \)[/tex]
- This is not correct because it suggests Maria hiked a total of 90 times, rather than covering 90 miles.
- Option 2: [tex]\( 5x - 10y = 90 \)[/tex]
- This equation does not correctly represent the total distance hiked. It would imply Maria hiked [tex]\( 5x \)[/tex] miles minus [tex]\( 10y \)[/tex], which doesn’t make sense in this context.
- Option 3: [tex]\( 90 - 10y = 5x \)[/tex]
- We start from [tex]\( 5x + 10y = 90 \)[/tex].
- Rearrange it to isolate [tex]\( 5x \)[/tex] on one side:
[tex]\[ 5x = 90 - 10y \][/tex]
- Option 4: [tex]\( 90 + 10y = 5x \)[/tex]
- This equation also doesn’t make sense in our context of total miles.
Therefore, the correct and equivalent rearranged form of the equation [tex]\( 5x + 10y = 90 \)[/tex] is:
[tex]\[ 90 - 10y = 5x \][/tex]
### Conclusion:
The correct equation that can be used to find the number of times Maria hiked the mountain trail and the canal trail, given the total distance of 90 miles, is:
[tex]\[ \boxed{90 - 10y = 5x} \][/tex]
### Step-by-Step Solution:
1. Identify the 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.
2. Set Up the Equation:
Maria hiked a total of 90 miles combining both trails. For each hiking trip:
- Each time Maria hikes the mountain trail, she covers 5 miles.
- Each time Maria hikes the canal trail, she covers 10 miles.
Therefore, the total distance covered when hiking both trails can be expressed as:
[tex]\[ 5x + 10y = 90 \][/tex]
3. Simplify the Equation:
We can simplify the equation by organizing it in different forms. One way to clearly express [tex]\( x \)[/tex] in terms of [tex]\( y \)[/tex] could be rearranging the given equation.
Let's look at the choices and find their equivalence:
- Option 1: [tex]\( x + y = 90 \)[/tex]
- This is not correct because it suggests Maria hiked a total of 90 times, rather than covering 90 miles.
- Option 2: [tex]\( 5x - 10y = 90 \)[/tex]
- This equation does not correctly represent the total distance hiked. It would imply Maria hiked [tex]\( 5x \)[/tex] miles minus [tex]\( 10y \)[/tex], which doesn’t make sense in this context.
- Option 3: [tex]\( 90 - 10y = 5x \)[/tex]
- We start from [tex]\( 5x + 10y = 90 \)[/tex].
- Rearrange it to isolate [tex]\( 5x \)[/tex] on one side:
[tex]\[ 5x = 90 - 10y \][/tex]
- Option 4: [tex]\( 90 + 10y = 5x \)[/tex]
- This equation also doesn’t make sense in our context of total miles.
Therefore, the correct and equivalent rearranged form of the equation [tex]\( 5x + 10y = 90 \)[/tex] is:
[tex]\[ 90 - 10y = 5x \][/tex]
### Conclusion:
The correct equation that can be used to find the number of times Maria hiked the mountain trail and the canal trail, given the total distance of 90 miles, is:
[tex]\[ \boxed{90 - 10y = 5x} \][/tex]
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