Word Problem:
Scenario: Alex is training for a local soccer tournament. He has set a goal to improve his overall fitness and skills.
Problem Statement:
During his training sessions, Alex runs a total of \( x \) kilometers each week. He runs three times a week: on Monday, Wednesday, and Friday. On Monday, he runs double the distance he runs on Wednesday, while on Friday, he runs 5 kilometers more than he does on Wednesday.
If Alex runs a total of 35 kilometers in one week, how far does Alex run on each of the three days?
Step-by-Step Solution:
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Define the Variables:
- Let \( w \) = the distance Alex runs on Wednesday (in kilometers).
- Then, the distance Alex runs on Monday will be \( 2w \) (twice Wednesday).
- The distance Alex runs on Friday will be \( w + 5 \) (5 km more than Wednesday).
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Set Up the Equation:
- The total distance Alex runs in a week is the sum of the distances run on each day: \[ x = (Distance \ on \ Monday) + (Distance \ on \ Wednesday) + (Distance \ on \ Friday) \]
- So we can set up the equation: \[ 2w + w + (w + 5) = 35 \]
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Simplify the Equation:
- Combine like terms: \[ 2w + w + w + 5 = 35 \] \[ 4w + 5 = 35 \]
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Solve for \( w \):
- Subtract 5 from both sides: \[ 4w = 35 - 5 \] \[ 4w = 30 \]
- Divide both sides by 4: \[ w = \frac{30}{4} = 7.5 \]
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Find the Distances for Each Day:
- Now that we have \( w \), we can find the distances for each day:
- Wednesday: \[ w = 7.5 \text{ km} \]
- Monday: \[ 2w = 2 \times 7.5 = 15 \text{ km} \]
- Friday: \[ w + 5 = 7.5 + 5 = 12.5 \text{ km} \]
- Now that we have \( w \), we can find the distances for each day:
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Conclusion:
- Alex runs 15 km on Monday, 7.5 km on Wednesday, and 12.5 km on Friday.
Summary of the Distances:
- Monday: 15 km
- Wednesday: 7.5 km
- Friday: 12.5 km
Thus, Alex meets his training goal of running a total of 35 kilometers during the week.
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