The price of a book was increased by 20\% to \30$. What was the original price, in dollars… — SAT

The price of a book was increased by $20\%$ to $\$30$ . What was the original price, in dollars, of the book?

The original price of the book was $25.

The correct answer is the price of

25. Let

represent the original price. Since the price was increased by

20\%

, the new price is

120\%

of

, or

1.20x

. Setting up the equation

1.20x = 30

and dividing both sides by

1.20

gives

x = 25$.

Set up an equation representing the percent increase. Let

x

represent the original price of the book. A

20\%

increase means the final price is

120\%

of the original price.

1.20x = 30

To find the original price, we must relate the original price, the percent increase, and the final price.

Solve for

x

by dividing both sides of the equation by

1.20

x = \frac{30}{1.20} = 25

Dividing isolates the variable

x

to find the original price.

Solving for the initial value after a percentage increase.

Question