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?

Which equation represents the scenario?

Answer 1

let number of hours be x

Celeste charges an initial fee of $5.00, and an hourly rate of $7.25.

C =5+7.25x...................(1)

Dora has an initial fee of $10.25, and an hourly rate of $6.50.

D=10.25+6.50x.................(2)

if the cost is same, equating equations (1) and (2)

5+7.25x=10.25+6.50x

7.25x-6.50x=10.25-5

0.75x = 5.25

x=7

so 7 hours is the answer

Answer 2

We can see that as the number of hours increase the charge also increase

Let x be the number of hours

The function denoting the scenario for Celeste

f(x)=
`5+7.25x`

The function denoting the scenario for Dora

g(x) =
`10.25+6.5x`

Now we need to know the time or number of hours x, when both the functions will give us the same value , that is f(x)=g(x)

`5+7.25x=10.25+6.5x`

`7.25x-6.5x=10.25-5.00`

`0.75x=5.25`

`x=(5.25)/(0.75)`

x=7

Hence at 7 hours of instruction both the instructors will get the same cost