Question

Membership warehouse clubs offer shoppers low​ prices, along with rewards of cash back on club purchases. If the yearly fee for a warehouse club membership is​ $100 and the reward rate is 2​% on club purchases for the​ year, then the linear equation y=100−0.02x models the actual yearly cost of the membership​ y, in dollars. Here x represents the yearly amount of club​ purchases, also in dollars.

​a) Determine the actual yearly cost of the membership if club purchases for the year
are ​$1500.
​b) What amount of club purchases would reduce the actual yearly cost of the membership
to ​$47​?
​c) How much would a member have to spend in yearly club purchases to reduce the
yearly membership cost to​ $0?

a) The actual yearly cost of the membership if club purchases for the year are ​$1500 is ​$___.

​(Simplify your answer. Type an integer or a​ decimal.)

Answer 1

a)100-.02(1500)=100-30=$70
b)100-47=53
53/.02=$2650 in purchases
c)100/.02=$5000 in purchases
a)Actual price of membership with $1500=$70
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Answer 2

A. $70

B. $2,650

C. $5,000

D. $70

Explanation:

We are given that,

The relation between the yearly cost of membership 'y' and the yearly club purchases 'x' is given by,
`y=100-0.02x`

A. It is given that the yearly club purchases is $1500 i.e. x= 1500.

So, we have,

`y=100-0.02x` i.e.
`y=100-0.02* 1500` i.e.
`y=100-30` i.e. y= 70.

So, the yearly cost of membership is $70.

B. It is given that the yearly cost of membership is $47 i.e. y= 47.

So, we have,

`y=100-0.02x` i.e.
`47=100-0.02x` i.e.
`0.02x=100-47` i.e.
`0.02x=53` i.e. x= 2,650

Thus, required club purchases would be $2,650

C. It is given that the yearly membership cost is $0 i.e. y= 0.

So, we have,

`y=100-0.02x` i.e.
`0=100-0.02x` i.e.
`0.02x=100` i.e. x= 5,000

Thus, required club purchases would be $5,000.

D. It is given that the yearly club purchases is $1500 i.e. x= 1500.

So, we have,

`y=100-0.02x` i.e.
`y=100-0.02* 1500` i.e.
`y=100-30` i.e. y= 70.

So, the yearly cost of membership is $70.