Question

A piano teacher schedules either 30-minute lessons or 60-minute lessons with her students. Last week, the teacher gave 9 lessons which lasted for a total of 7 hours. How many 30-minute lessons did the teacher give last week?

Answer 1

Let's use algebra to solve this problem. Let x be the number of 30-minute lessons that the teacher gave last week, and let y be the number of 60-minute lessons. We know that the teacher gave a total of 9 lessons, so we can write:

x + y = 9

We also know that the total time spent on lessons was 7 hours, which we can convert to minutes:

30x + 60y = 420

Now we have two equations with two unknowns, which we can solve using substitution or elimination. Let's use substitution:

x + y = 9 -> y = 9 - x

30x + 60y = 420 -> 30x + 60(9 - x) = 420

Simplifying and solving for x:

30x + 540 - 60x = 420

-30x = -120

x = 4

Therefore, the teacher gave 4 30-minute lessons last week. To find the number of 60-minute lessons, we can substitute x = 4 into either equation:

x + y = 9 -> y = 9 - x -> y = 9 - 4 -> y = 5

So the teacher gave 5 60-minute lessons last week.