asked 128k views
2 votes
A hair salon charges a fixed rate of $25.00 for a haircut and an additional $15 for any other services. Formulate a function to model the cost of services at the salon and then evaluate the function to determine the cost for a haircut, shampoo, highlight, and blow dry.

asked
User Lucchi
by
8.3k points

1 Answer

3 votes

Answer:

c = 15x + 25

$75

Explanation:

Before we "math" it, let's think about it for a minute.

If you get just a haircut it's $25. Cool.

Oh, you want highlights too? That's an extra $15. (Sounds like addition, doesn't it?)

So already we can build a little function:

total cost = cost of haircut + cost of highlights

But oh, you want highlights and shampoo and dry? Hmmm, maybe this:

cost = haircut + highlights + shampoo + dry

Almost there, I promise. They made it easy for us because all those "extras" cost the same. So let's just call that cost "e" for "extras":

c = h + e + e + e Simplify to:

c = h + 3e

But that's for the specific case of getting all three extras (which is the last thing they ask).

More generically, we won't know how many extras the customer will want until they tell us. So since that's an "unknown," let's call it x.

Now in the equation, h & e are constants, they don't change. Where I had the 3, that's where x goes, because it's an unknown until the customer tells us what they want. And c is a variable that will be the answer to the specific situation. So:

c = h + ex Then to put that in the more-normal form:

ex + h = c Nothing changed there, just the order.

We know what h and e are, so plug them in:

15x + 25 = c

Do you see all the real-world pieces there? $25 is the base cost, the cost of just a haircut. Then if you want extras you have to pay $15 each for those, so that's a multiplication term. Add them up to get total cost.

So for the last part of the question for the customer who got a haircut plus 3 services, the stylist does this in their head, substituting 3 for x:

c = 15x + 25

c = 15(3) + 25 = 45 + 25 = $70

I hope the discussion helped, rather than just tell you the answer.

Take care.

answered
User Gregology
by
8.3k points
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