Question

Tom's Hat Shoppe increased all original prices by $25\%.$ Now the shoppe is having a sale where all prices are $20\%$ off these increased prices. Which statement best describes the sale price of an item?

The sale price is $5\%$ higher than the original price.

The sale price is higher than the original price, but by less than $5\%.$

The sale price is higher than the original price, but by more than $5\%.$

The sale price is lower than the original price.

The sale price is the same as the original price.

Solution:

Increasing by $25\%$ multiplies the price by $1.25,$ and then taking $20\%$ off multiplies by $0.80.$

The overall factor is $1.25 \times 0.80 = 1.00,$ so the sale price equals the original price.

Thus, the correct answer is E .

1988 AMC 8 Problem 22

Solution:

Problem 22 in Other Years