# 1. If the price of the book at $14.99 was deemed to be too high, and was subsequently reduced to its old $11.99 price, what is the percentage change? 2. After a reduction of 14 ½ % off the marked...

1. If the price of the book at $14.99 was deemed to be too high, and was subsequently reduced to its old $11.99 price, what is the percentage change?

2. After a reduction of 14 ½ % off the marked price, a pair of boots sold for $120. What was the marked price?

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### 3 Answers

The price of a book initially selling for $14.99 was later reduced to $11.99.

The percent change in the price is `((14.99 - 11.99)/14.99)*100 ~~ 20.01%`

The price of a pair of boots after a discount of 14.5% is $120. The original marked price was `120/(1 - 0.145) ~~ $140.35`

1. To find the percentage change, we need to divide the amount changed by the original amount.

The amount changed is `14.99-11.99 = 3`

And the orignial amount is `14.99`

So: `3/14.99 ~~ .2001`

Multiply by 100 to find the percentage:

`.2001 * 100 = 20.01%`

2. If the price was reduced 14.5%, then we know that the current price, $120, is 85.5 % or (100 - 14.5)% of the original price.

This means that the marked price multiplied by 85.5% equals $120.

Knowing this we can set up an equation:

.855 *(marked price) = 120

Divide 120 by .855:

`120/.855 = 140.35`

Answer: The marked price was $140.35

1) What I did is found out what equaled 1% of 14.99. So divided 14.99/100 which equals 0.1499. So I wanted to find out how much pertage out of 100 was the 11.99. So 11.99/0.1499 equals 79.98%. **So the difference is approximatley 20% difference**. To double check, if you round the numbers to the whole number, 14.99 is 15, and 11.99 is 12. 20% of 15 is 3 dollars so 15-3 = 12.

2) To find the total price I multiplied it by itself plus the extra 14.5% that was marked off. So $120*1.145= **$137.40, which is the marked price before the reduction**.