Max has a one hour piano lesson twice a week, Hanna only has a one hour lesson every second week. The pianolessons run over a particular number of weeks. How many weeks is this, if during this time Max has 15 more hoursof lessons than Hanna?(A) 30 Weeks (B) 25 Weeks (C) 20 Weeks (D) 15 Weeks (E) 10 Weeks
Question
Max has a one hour piano lesson twice a week, Hanna only has a one hour lesson every second week. The pianolessons run over a particular number of weeks. How many weeks is this, if during this time Max has 15 more hoursof lessons than Hanna?(A) 30 Weeks (B) 25 Weeks (C) 20 Weeks (D) 15 Weeks (E) 10 Weeks
Solution
Let's break down the problem:
- Max has two one-hour piano lessons per week. This means he has 2 hours of piano lessons per week.
- Hanna has a one-hour lesson every second week. This means she has 0.5 hours of piano lessons per week.
- We know that Max has 15 more hours of lessons than Hanna over a certain number of weeks.
Let's denote the number of weeks as x. We can set up the following equation to solve for x:
2x (the total hours of lessons Max has) = 0.5x (the total hours of lessons Hanna has) + 15 (the extra hours Max has)
Solving for x, we get:
2x - 0.5x = 15 1.5x = 15 x = 15 / 1.5 x = 10
So, the number of weeks is 10. The answer is (E) 10 Weeks.
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