Mr. Davis works as a barber, and he's thinking about raising his rates. He currently charges $20 for a haircut, and he does about 250 haircuts per month. He estimates that for every additional dollar he charges, he will do 8 fewer haircuts per month.If Mr. Davis raises the price of a haircut by x dollars, find an expression for f(x), the new price of a haircut.f(x)=Next, find an expression for g(x), the number of haircuts Mr. Davis estimates he will do in a month if he raises the price by x dollars.g(x)=Which function can you use to find the total amount of money Mr. Davis can expect to bring in from haircuts in a month if he raises the price by x dollars?
Question
Mr. Davis works as a barber, and he's thinking about raising his rates. He currently charges $20 for a haircut, and he does about 250 haircuts per month. He estimates that for every additional dollar he charges, he will do 8 fewer haircuts per month.If Mr. Davis raises the price of a haircut by x dollars, find an expression for f(x), the new price of a haircut.f(x)=Next, find an expression for g(x), the number of haircuts Mr. Davis estimates he will do in a month if he raises the price by x dollars.g(x)=Which function can you use to find the total amount of money Mr. Davis can expect to bring in from haircuts in a month if he raises the price by x dollars?
Solution
First, let's find an expression for f(x), the new price of a haircut.
Mr. Davis currently charges $20 for a haircut. If he raises the price by x dollars, the new price will be the current price plus x dollars. So, the expression for f(x) is:
f(x) = 20 + x
Next, let's find an expression for g(x), the number of haircuts Mr. Davis estimates he will do in a month if he raises the price by x dollars.
Mr. Davis currently does 250 haircuts per month. He estimates that for every additional dollar he charges, he will do 8 fewer haircuts per month. So, if he raises the price by x dollars, he will do 8x fewer haircuts. The expression for g(x) is:
g(x) = 250 - 8x
To find the total amount of money Mr. Davis can expect to bring in from haircuts in a month if he raises the price by x dollars, you can use the function h(x) = f(x) * g(x), where f(x) is the new price of a haircut and g(x) is the number of haircuts he will do.
So, h(x) = (20 + x) * (250 - 8x)
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