Math 115 - Week 9 Application Assignment Please answer the following questions i
ID: 3143059 • Letter: M
Question
Math 115 - Week 9 Application Assignment
Please answer the following questions in the spaces provided. Show your work to receive full credit.
A) Parents with young babies buy a lot of diapers (to say the very least), so getting the best deal is pretty important. Comparing prices can be harder than you would think, though - retailers don’t all sell diapers in the same size boxes. A recent check of prices on Pampers Swaddlers in Size 1 revealed the following:
Amazon.com: 234 diapers for $46.99
Local Store: 160 diapers for $34.99
Find the unit price for each box of diapers and use it to decide which is the best deal. (There’s free shipping, so don’t worry about shipping or tax.)
B) Amazon offers an interesting deal: if you pay $79 per year to join their “Amazon Mom” club, you get 20% off all diaper purchases. What would the $46.99 box of diapers cost with that discount?
C) Write an equation that provides the total cost C of buying x boxes of diapers in one year with the Amazon Mom membership.
D) Use your equation to find the cost of buying 10 boxes of diapers in a year if you join Amazon Mom.
E) Write another equation that provides the total cost C of buying x boxes of diapers in one year from Amazon without being a member of Amazon Mom.
F) Use your equation from Question 5 to find the cost of buying 10 boxes of diapers in a year without the Amazon Mom membership.
G) The equations you wrote in Questions 3 and 5 form a system of equations. Solve that system and use your result to find how many boxes of diapers you’d need to buy in a year for the two costs to be the same. What would the cost be then?
H) Under what circumstances would you want to join Amazon Mom to buy diapers? (Well, obviously having a baby would be one of those circumstances. What other ones?)
Explanation / Answer
Ans(A):
cost calculation for Amazon.com:
cost of 234 dipers = $46.99
cost of 1 diper = $46.99/234= $0.200811965812
Hence cost of 1 diper from Amazon.com is approx $0.20
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cost calculation Local store:
cost of 160 dipers = $34.99
cost of 1 diper = $34.99/160= $0.2186875
Hence cost of 1 diper from Local Store is approx $0.22
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Ans(B):
fixed price for membership = $79
purchase = $ 46.99
20% discount means you have to pay only 80% of purchase which is =
= 0.80*46.99= $37.592
so total cost after discount= 79+37.592= $116.592
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Ans(C):
Let number of boxes purchased per year = x
cost of 1 diper without discount = $0.20 ( from part A)
cost of x dipers without discount = $0.20x
20% discount means you have to pay only 80% of purchase which is = 0.80*0.20x =$0.16x for 1 box of diper
so total cost after discount and membership = 79+0.16x
Hence cost equation will be
C=0.16x+79
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Ans(D):
we will use equation from part C
C=0.16x+79
10 dipers means x=10
C=0.16x+79=0.16*10+79 = $80.60