Question

The new Perry Hotter book will have a cover price of $25. The local bookstore is offering two discounts $4.00 off and 20% off. A clever shopper realizes that the prices will be different depending on the order in which she claims her discounts. How much more money will she save by taking the better valued approach rather than the other approach? Express your answer in cents.

Answer 1

The shopper will save 80 cents more by taking the better-valued approach.

Step-by-step explanation:

To find out how much more money the shopper will save by taking the better-valued approach, we need to calculate the final price using both discount approaches and compare them.

1. Approach 1: First, apply the $4.00 discount and then the 20% off discount. Start with the original price of $25. Subtract $4.00 to get $21.00. Then, apply the 20% discount by multiplying $21.00 by 0.20, which gives a $4.20 discount. Subtract $4.20 from $21.00 to get the final price of $16.80.
2. Approach 2: First, apply the 20% discount and then the $4.00 discount. Start with the original price of $25. Apply the 20% discount by multiplying $25.00 by 0.20, which gives a $5.00 discount. Subtract $5.00 from $25.00 to get $20.00. Then, subtract $4.00 from $20.00 to get the final price of $16.00.

The shopper will save $16.80 - $16.00 = $0.80 more by taking the better-valued approach. To express this in cents, multiply $0.80 by 100, which answers 80 cents.

Answer 2

The first way is to do 25% off then $4.00 off.
25% of 25 is $6.25.
25 - 6.25 = 18.75
Deduct the $4.00 discount.
18.75 - 4 = $14.75

The second way is $4.00 off then 25% off.
Subtract the $4.00 discount.
25 - 4 = 21
25% of 21 is 5.25.
21 - 5.25 = $15.75

The final cost for the first way is exactly $1 more, or 100 cents.
Hope this helps!