Celeste and Dora both offer guitar lessons. Celeste charges an initial fee of $5.00, and an hourly rate of $7.25. Dora has an initial fee of $10.25, and an hourly rate of $6.50. The equation 7.25h + 5 = 6.5h + 10.25 represents the scenario.

At how many hours of instruction will the cost be the same for both instructors?

Question

Celeste and Dora both offer guitar lessons. Celeste charges an initial fee of $5.00, and an hourly rate of $7.25. Dora has an initial fee of $10.25, and an hourly rate of $6.50. The equation 7.25h + 5 = 6.5h + 10.25 represents the scenario.

At how many hours of instruction will the cost be the same for both instructors?

Mercury · Answer

since the equation has set Celeste's fees and Dora's fees equal to each other, you simply need to solve the equation for h

7.25h + 5 = 6.5h + 10.25

start by subtracting 6.5h from both sides to get all the h terms on one side
subtract 5 from both sides to get the constants on the other side
then divide by the coefficient of h