Question

Leda and Thanh both offer piano lessons. leda 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?

Answer 1

Leda and Thanh's piano lesson prices will be the same after 3 hours of instruction. This is found by setting up equations for each instructor's pricing structure and solving for the number of hours where both costs are equal.

Step-by-step explanation:

To determine at how many hours of instruction the price for each instructor will be the same, we set up an equation for each instructor where the total cost is the sum of the initial fee plus the hourly rate multiplied by the number of hours. For Leda, the cost equation is given by C = 8.50 + 11.00h, and for Thanh, the cost equation is given by C = 10.00 + 10.50h. To find the number of hours where both instructors charge the same amount, we set the two equations equal to each other:

8.50 + 11.00h = 10.00 + 10.50h

Subtract 10.50h from both sides:

8.50 + 0.50h = 10.00

Now, subtract 8.50 from both sides:

0.50h = 1.50

Finally, divide both sides by 0.50 to solve for h:

h = 3

The price for each instructor will be the same after 3 hours of instruction.