Answer:
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.
