A clothing store is having a sale in which you can take 50 o

A clothing store is having a sale in which you can take $50 off the cost of any coat in the store. The store also offers 10% off your entire purchase if you open a charge account. You decide to open a charge account a buy a coat. Set up a function for the total cost P on an n-dollar Purchase, Provided only the $50 discount is applied._____Set up a function for the total cost C on a n-dollar purchase, provided only the 10% discount is applied._____Write an equation to represent (P. C) (n)._____Write an equation to represent (C. P) (n)._____Find the sale price of a $175 coat when $50 is subtracted before the 10% discount is applied._____Which function: (P. C) (n), or (C. P) (n) can be used to accurately calculated the answer to (e)?_____Why doesn\'t the store apply the 10% discount before subtraction $50?_____Explain clearly._____

Solution

Ans(a):
P(n)=n-50
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Ans(b):
10% discount is applied means you have to pay only 90% so total cost is given by
C(n)=0.90(n)
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Ans(c):
P(n)=n-50
C(n)=0.90(n)
(PoC)(n)=P(C(n))=P(0.90(n))=0.90(n)-50
(PoC)(n)=0.90(n)-50
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Ans(d):
P(n)=n-50
C(n)=0.90(n)
(CoP)(n)=C(P(n))=C(n-50)=0.90(n-50)
(CoP)(n)=0.90(n-50)
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Ans(e):
first $50 discount applied so unpaid price =$175-$50=$125
then 10% discount applied means you have to pay 90% of $175 which is = 175*0.90=$157.5
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Ans(f):
say 10% discount applied first then amount then total cost is given by
(PoC)(175)=0.90(175)-50=$107.5
which is less than price $157.5 that you will need to pay when $50 discount applied first.
obviously store wants more money. Hence store doesn\'t apply 10% discount first.