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. At how many hours of instruction will the cost for each instructor be the same?

Answer 1

To determine when the cost of guitar lessons from Celeste and Dora will be the same, set up and solve the equations representing each instructor's charges. By doing so, we find that after 7 hours of instruction, the costs will be equal.

Step-by-step explanation:

We are asked to determine at what point the cost of guitar lessons from two different instructors, Celeste and Dora, will be the same. To find this, we need to set up two equations that represent the total cost of the lessons from each instructor and solve for the number of hours where the costs are equal.

Celeste's charges can be expressed as y = 5 + 7.25x, where y is the total cost and x is the number of hours. Similarly, for Dora, the charges can be expressed as y = 10.25 + 6.50x.

By setting these two equations equal to each other:

5 + 7.25x = 10.25 + 6.50x

Now we solve for x:

7.25x - 6.50x = 10.25 - 5

0.75x = 5.25

x = 5.25 / 0.75

x = 7

So, after 7 hours of instruction, the cost for each instructor will be the same.

Answer 2

Just for walking in the door, before any lessons,

Celeste . . . $5.00
Dora. . . . . $10.25

For 'H' hours of instruction,

Celeste . . . $7.25 x H
Dora . . . . . $6.50 x H .

Total cost to take lessons from

Celeste . . . 5 + 7.25H
Dora . . . . . 10.25 + 6.5 H

What is the number of hours ' H ' when both of their total costs
would be the same ?

5 + 7.25H = 10.25 + 6.5H

Subtract 6.5H from each side: 5 + 0.75H = 10.25

Subtract 5 from each side: 0.75H = 5.25

Divide each side by 0.75 : H = 5.25/0.75 = 7 hours

After 7 hours of instruction, Celeste's student and Dora's student
have both paid $55.75 . After that, Celeste's student pays 75¢
more for each hour of instruction than Dora's student pays.