Problem Solving

Cindy has her eye on a sundress but thinks it is too expensive. It goes on sale for 15% less than the original price. Before Cindy can buy the dress, however, the store raises the new price by 25%. If the dress cost $68 after it went on sale for 15% off, what is the difference between the original price and the final price?

A)$0.00

B)$1.00

C)$3.40

D)$5.00

E)$6.80

OAD

Cindy has her eye on a sundress but thinks it is too expensive. It goes on sale for 15% less than the original price. Before Cindy can buy the dress, however, the store raises the new price by 25%. If the dress cost $68 after it went on sale for 15% off, what is the difference between the original price and the final price?
A) $0.00
B) $1.00
C) $3.40
D) $5.00
E) $6.80

15% discount = 15/100 = 3/20.
The denominator here implies that the original price is almost certainly a multiple of 20 just a bit greater than the discounted price.
Since the discounted price = 68, the original price is probably 80:
80 less 3/20 = 80 - (3/20)80 = 80-12 = 68.
Success!
Discounted price increased by 25% = 68 + (1/4)68 = 68 + 17 = 85.
Difference between the final price and the original price = 85-80 = 5.

The correct answer is D.

Algebraically:
Since the 15% discount is equal to 3/20 of the original price, the discounted price is equal to 17/20 of the original price:
68 = (17/20)x
x = 68(20/17) = 80.
Discounted price increased by 25% = 68 + (1/4)68 = 68 + 17 = 85.
Difference between the final price and the original price = 85-80 = 5.

One other way of seeing this:

Original price: $x
First adjusted price: $68
Second adjusted price: $y

We know that 68 = x - (15% of x), or 68 = .85x, or 6800 = 85x, which gives x = 80.

We also know that y = 68 + (25% of 68) = 85. So y = 85, and y - x = $5.