Ieda and Thanh both offer piano lessons. Ieda charges an initial fee of $8.50 and an hourly rate of $11.00. Thanh charges an initial fee of $10.00 and an hour rate of $10.50. At how many hours of instruction will the price for each instructor be the same?

2 hours

3 hours

20 hours

30 hours

Ieda: $11.00 (hourly price) + $8.50 (initial fee) = $19.50 (for 1 hour)

Thanh: $10.50 (hourly price) + $10.00 (initial fee) = $20.50 (for 1 hour)

Now that you have the price for 1 hour including the initial fee, now you need to find the price for each hour after that. Here's how I did that:

I created a graph that looked like this:

Hours: 1 2 3

Ieda: 19.50 30.50 41.50

Thanh: 20.50 31.00 41.50

Here's how I figured out the price for each hour:

Ieda:

Hour 1 (including initial price):

$11.00 + $8.50 = $19.50

Hour 2 (excluding initial price) : Only add the hourly price after Hour 1!

$19.50 + $11.00 = $30.50

Hour 3 (excluding initial price):

$30.50 + $11.00 = $41.50

Thanh:

Hour 1 (including initial price):

$10.50 + $10.00 = $20.50

Hour 2 (excluding initial price):

$20.50 + $10.50 = $31.00

Hour 3 (excluding initial price):

$31.00 + $10.50 = $41.50

So, looking at the graph, their prices are the same once each instruction reaches 3 hours. ($41.50)

11h+8.50=10.50h+10

Solve for h

h=3 hours ... answer