The tuition costs, C, for a local community college are modeled by C(h) = 250 + 200h, where h represents the number of credit hours taken. The local state university has tuition costs, S, modeled by the function S(h) = 300 + 180h. How many credit hours will a student have to take for the two tuition costs to be equal? Round the answer to the nearest tenth of an hour. 250 + 200h = 300 + 180h 250 + 200h = 300 + 180h − 180h − 180h 250 + 20h = 300 h = credit hours

To solve how many credit hours will a student have to take
for the two tuition costs to be equal, the two functions should be equated and
solve for the number of hours

C (h) = S (h)

250 + 200h = 300 + 180h

200h – 180h = 300 – 250

20h = 50

H = 2.5 credit hours

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MrRoyal MrRoyal · Answer 2 · 2021-11-02T07:56:47-04:00

The required equation is: \(\mathbf{150 + 200h = 300 + 180h}\) and the number of credit hours is 7.5

The functions are given as:

\(\mathbf{C(h) = 250 + 200h}\)

\(\mathbf{S(h) = 300 + 180h}\)

When the two tuition costs are equal, we have:

\(\mathbf{C(h) = S(h)}\)

This gives

\(\mathbf{150 + 200h = 300 + 180h}\)

Collect like terms

\(\mathbf{ 200h -180h= 300 -150 }\)

\(\mathbf{ 20h= 150 }\)

Divide both sides by 20

\(\mathbf{ h= 7.5 }\)

Hence, the required equation is: \(\mathbf{150 + 200h = 300 + 180h}\) and the number of credit hours is 7.5