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?

after 3 hours of instruction.

Step-by-step explanation:

First, start by setting up the equation.

Leda charges an initial fee, meaning this fee is only going to be one time. However, there is an hourly rate of 11. Since we do not know how many hours these piano lessons are going to last, we put a variable (I will use x), after this number.

The initial fee is 8.50. There needs to be a variable after 11 because that is the number we don't know.

The equation for Leda's lessons are 8.50+11.00x.

Now, we need to find out what the equation for Thanh's lessons are going to be, because we're going to be setting both equations equal to each other to find out when they cost the same. At the moment both equal each other, is when they are the same amount.

Thanh's equation also has an intial fee and an hourly rate. So, the equation will be

10.00+10.50x.

Now we solve.

8.50+11.00x = 10.00+10.50x

First, subtract from both sides. We will do the numbers without variables first.

8.50+11.00x = 10.00+10.50x

-8.50               -8.50

0     +11.00x =   1.50 +10.50x

Then, subtract the x's. (taking away the zero because it is equivalent to nothing)

11.00x =   1.50 +10.50x

- 10.50x            -10.50x

0.50x = 1.50

Lastly, to find out the answer, we divide.

1.50/0.50= 3.

To check your answer, you can plug into the original equation.

8.50+11.00 times 3 = 10.00+10.50 times 3

Both sides equal 41.50, meaning they are equal to each other!