Please help me solve the questions to these story problems:      ""You have a coupon for $50 off your camera purchase of $100 or more at Zeke's Camera World."" 1.    Write a function...

Please help me solve the questions to these story problems:

     ""You have a coupon for $50 off your camera purchase of $100 or more at Zeke's Camera World.""

1.    Write a function relating a camera's purchase price after coupon, y, to the retail price, x.  Give the domain of this function.

   "" An online retailer currently offers a 40% discount on cameras.""

2.    Write a function relating a camera's purchase price, y, to the retail price, x.  Give the domain of this function.

3.  How do I graph the functions from #1 and #2 using a scale of 25 for both axes?  Will you show this on a graph please.

4.  If you use the coupon in problem #1, what is the minimum  your camera purchase will cost (before taxes)?  Please show steps to solve.

5.  What is the point of intersection?  Show calculations to support  your observation.

6.  For each of the following retail prices, which places offer the better purchase price.  Show how to solve as well.

$75         Zeke's            Online             None

$100        Zeke's           Online             None

$125       Zeke's            Online              None

$150       Zeke's            Online               None

Please show steps.

Thanks and Happy New Year!

Asked on by marley112

1 Answer | Add Yours

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baxthum8 | High School Teacher | (Level 3) Associate Educator

Posted on

1. Write a function relating a camera's purchase price after coupon, y, to the retail price, x. Give the domain of this function.

Retail price = $x over $100

Coupon  = $50

y = purchase price after coupon

`y = x - 50` where x `>=100`

`{x:x>=100}`

2.  40% discount 

Camera remains 60% of original:  `y = .6x`

{x:x`>=0}`

 3.  #1 graph in red, however only graph from x >= 0 should be graphed,  #2 graph in blue.  Graph should be from x >=0

4.  If using the coupon, the minimum cost a purchase could be is:

y = 100 - 50  $100 is the least amount at which you are allowed to use the coupon.

y = 50  Therefore the lowest cost could be $50.

5.  The point of intersection from the graph is original retail price of $125, a discount of 40% or $50 off yields a price of $75.

y = x - 50 and y = 0.6x

Use equal values method to solve.

`x - 50 = 0.6x `

`-50 = -0.4x`

`x = 125`

`Substitute 125 for x into 1 of the original problems `

`125-50 = 75 `

`y = 75 `

6. Retail price $75 Zeke's = $75 Online = 75(0.6) = 45

Online best deal for $75

Retail price:  $100       Zeke's = 100-50 = $50        Online = 100(0.6) = 60

Zeke's is best deal for $100

Retail price: $125 Zeke's = 125-50 = 75 Online = 125(.6) = 75

Same price at either place for $125

Retail price of $150 Zeke's = 150 - 50 = $100 Online = 150(0.6) = 90

For $150 the best deal is online.

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