SOLUTION: MR. Alba rents studio space at a music school to teach voice lessons. He charges $30 for a 30-minute lesson and pays a studio rental fee of $10 per hour. Mr. Alba has approximately

Question 1106704: MR. Alba rents studio space at a music school to teach voice lessons. He charges $30 for a 30-minute lesson and pays a studio rental fee of $10 per hour. Mr. Alba has approximately $55 per month in business expenses. Let n represent the number of hours he teaches each month. Which function represents Mr. Alba's monthly income?
A. f(n)= 30n-55
B. f(n)= 20n-55
C. f(n)= 50n-55
D. f(n)= 25n+55

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
he shells out 50 dollars a month because of business expenses.

he pays 10 dollars an hour for the use of the studio.

he earns 30 dollars for a half hour session.
multiply that by 2 and he earns 60 dollars per hour.

let n equal the number of hours he teaches per month.

his revenue for the month is 60 * n.

his cost for the month is 10 * n + 55

income (or profit) is equal to revenue minus cost.

you get incomed = 60 * n - 10 * n - 55

combine like terms to get income = 50 * n - 55 which can also be written as income = 50n - 55.

let f(n) represent his income.

your equation becomes f(n) = 50n - 55.

that looks like selection c.

they threwa curve in this problem by telling you that he earned 30 dollars per half hour and that he paid 10 dollars per hour.

you needed to translate everything to the same quantity.

30 dollars had to become 60 dollars per hour.

then all the per hour costs were identified correctly.

you had revenue of 60 dollars per hour and costs at 10 dollars per hour.
the net income from that was 50 dollars per hour.

i almost missed that.
it helps to always check if you get everything in the same unit of measure.
in this case it's per hour.

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