Question

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

Answer 1

Cristobal needs to spend at least $115.20 in a year for the second bookstore's membership to be the better value. Option A, $115.21, is the nearest given option.

Step-by-step explanation:

To determine when the membership at the second bookstore is a better value, we need to calculate the total savings Cristobal would get from each membership and then see at what spending amount the second bookstore's savings would surpass the first bookstore's savings.

Let's denote the amount Cristobal spends in a year as x. At the first bookstore, he pays $17.05 for the membership and saves 15%. At the second bookstore, he pays $28.57 for the membership and saves 25%.

Savings at the first bookstore would be: 0.15x

Savings at the second bookstore would be: 0.25x

We want to find the point where the second bookstore's total savings minus its membership fee is greater than or equal to the first bookstore's total savings minus its membership fee. This gives us:

0.25x - $28.57 ≥ 0.15x - $17.05

Solving for x:

• 0.25x - 0.15x ≥ $28.57 - $17.05
• 0.10x ≥ $11.52
• x ≥ $115.20

Hence, Cristobal needs to spend at least $115.20 in a year for the second bookstore's membership to be the better value. Looking at the options provided, the closest option to our calculated value is A. $115.21.

Answer 2

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.