# Thread: Discounted Price

1. ## Discounted Price

The price of a certain tv set is discounted by 10 percent, and the reduced price is then discounted by 10 percent. This series of successive discounts is equivalent to a single discount of

A. 20 percent
B. 19 percent
C. 18 percent
D. 11 percent
E. 10 percent

I decided to subtract 0.10 from 1. This led to 0.90.
I then decided to subtract 0.10 from 0.90. This led to 0.80.
I concluded that the answer must by 20 percent because 20 percent plus 80 percent is 100 percent.
So, 1 - 0.20 = 0.80.

The book's answer is B, however. My answer is A. Why is my answer wrong?

2. ## Re: Discounted Price

Let x = the original price of the TV set

First discount: x - 0.1x = 1x - 0.1x = (1 - 0.1)x = 0.9x

Second discount: 0.9x - 0.1(0.9x) = 0.9x - 0.09x = (0.9 - 0.09)x = 0.81x

You're left with 81% of the original price.

The equivalent single discount is (100%)x - (81%)x = (19%)x.

B. 19 percent

- - - - - - - - - - - - - - - - - - - - - OR - - - - - - - - - - - - - - - - - - - - - -

(0.9x)(0.9) = 0.81x

x - 0.81x = 1x - 0.81x = (1 - 0.81)x = 0.19x

(19%)x

B. 19 percent

3. ## Re: Discounted Price Originally Posted by harpazo I then decided to subtract 0.10 from 0.90. This led to 0.80.

The book's answer is B, however. My answer is A. Why is my answer wrong?
100 - .10(100) = 90
90 - .10(90) = 81

Your way assumes a 20% discount right away...

4. ## Re: Discounted Price Originally Posted by harpazo The price of a certain tv set is discounted by 10 percent, and the reduced price is then discounted by 10 percent. This series of successive discounts is equivalent to a single discount of

A. 20 percent
B. 19 percent
C. 18 percent
D. 11 percent
E. 10 percent

I decided to subtract 0.10 from 1. This led to 0.90.
I then decided to subtract 0.10 from 0.90. This led to 0.80. This is where you have gone wrong. You should be subtracting 10% of 0.90 (which is 0.09 not 0.10) from 0.90.
I concluded that the answer must by 20 percent because 20 percent plus 80 percent is 100 percent.
So, 1 - 0.20 = 0.80.

The book's answer is B, however. My answer is A. Why is my answer wrong?
See comment in red.

5. ## Re: Discounted Price

Thank you everyone.