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 in itial 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?
2 answers:
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
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)=
The function denoting the scenario for Dora
g(x) =
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)
x=7
Hence at 7 hours of instruction both the instructors will get the same cost
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