Cristobal is comparing the membership club fees at two different bookstores. At the first bookstore, it costs $17.05 annually to be a member of the club, but he will save 15% on all his purchases. At the second bookstore, it costs $28.57 annually to be a member of the club, but he will save 25% on all his purchases. How much does Cristobal need to spend in a year for the membership at the second bookstore to be the better value? A. $115.21 B. $144.00 C. $86.64 D. $132.48

A) Cristobal need to spend $115.2 in a year for the membership at the second bookstore to be the better value.

Step-by-step explanation:

Let x : Amount Cristobal needs to spend for 2nd membership to be better.

At First bookstore:

Member ship fee = $17.05

The savings on purchase = 15%

So, actual payment = x - (15% of x)

= x - 0.15 x = 0.85 x

So, the total payment in first bookstore

= Membership fee + Purchase payment

= $17.05 + 0.85 x

or, the amount paid at first book store = $17.05 + 0.85 x

At Second bookstore:

Member ship fee = $28.57

The savings on purchase = 25%

So, actual payment = x - (25% of x) = x - 0.125 x = 0.75 x

So, the total payment in first bookstore = $28.57 + 0.75 x

Now, payment made at second store >Payment at first store

⇒$28.57 + 0.75 x > $17.05 + 0.85 x

or, 18-57 - 17-05 > 0.85 x - 0.75 x

or, 0.10x < 11.52

or, x < 11.52/0.10 = 115.2

or, x < 115.2

Hence, Cristobal need to spend $115.2 in a year for the membership at the second bookstore to be the better value.