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Question 1087081: A cookie company charges $1.50 per cookie, plus a delivery fee of $1.
Write a function that represents the total price P (in dollars) as a function of c (number of cookies).
P(c)=
What is the total cost to purchase 2 cookies and have them delivered?
P(2)=
If I have $35, how many cookies can I have delivered?
c=
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! I'll write the answers first and explain how I got each answer.
The function is P(c) = 1.50*c + 1
When we plug c = 2 into the function we get P(2) = 4 meaning that it costs $4 to deliver 2 cookies
If you have $35, then you can have c = 22 cookies delivered
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We're told that it costs $1.50 per cookie and there's a flat fee of $1. This means that no matter how many cookies you order, you pay at least $1. If you order c cookies, then it costs 1.50*c dollars on top of the $1 paid in the flat fee. So that's why the first answer is P(c) = 1.50*c + 1
Once we have the function P(c) = 1.50*c + 1, we replace every copy of c with 2.
Then we use PEMDAS to evaluate
P(c) = 1.50*c + 1
P(2) = 1.50*2 + 1
P(2) = 3 + 1
P(2) = 4
So it costs $4 to deliver 2 cookies
The last part is where we take things in reverse. Instead of plugging in some number for c, we replace P(c) with a known cost and we solve for c itself. In this case, P(c) = 35 is the cost or budget we set aside.
So we go from
P(c) = 1.50*c + 1
to
35 = 1.50*c + 1
Solve for c to get...
35 = 1.50*c + 1
35-1 = 1.50*c + 1 - 1
34 = 1.50*c
1.50*c = 34
1.50*c/1.50 = 34/1.50
c = 22.6666666666667
Rounding down (not up) to the nearest whole number and we get c = 22. So we can afford to get 22 cookies if the budget is $35. Why do we round down? Because rounding up leads to P(c) being too costly and we go over budget. Look at how
P(c) = 1.50*c + 1
P(22) = 1.50*22 + 1
P(22) = 34
and we stay under budget but plugging in c = 23 leads to
P(c) = 1.50*c + 1
P(23) = 1.50*23 + 1
P(23) = 35.50
and we're 50 cents over budget. So c = 23 is too much. The highest amount we can order is c = 22.
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