Math Snap

STEP 1

Assumptions1. The discounted price of the book is $19.50. The discount rate is25%
3. The discount is calculated from the original price

STEP 2

First, we need to understand that the discounted price is the result of subtracting the discount from the original price. We can express this as a formula$$Discounted\, price = Original\, price - Discount$$

STEP 3

The discount is calculated as a percentage of the original price. We can express this as a formula$$Discount = Original\, price \\times Discount\, rate$$

STEP 4

Substituting the formula for the discount into the formula for the discounted price, we get$$Discounted\, price = Original\, price - (Original\, price \\times Discount\, rate)$$

STEP 5

We can simplify this formula by factoring out the original price$$Discounted\, price = Original\, price \\times (1 - Discount\, rate)$$

STEP 6

We can rearrange this formula to solve for the original price$$Original\, price = Discounted\, price / (1 - Discount\, rate)$$

STEP 7

Now, plug in the given values for the discounted price and discount rate to calculate the original price.
Original\, price = \($\)19.50 / (1 -25\%)

STEP 8

Convert the percentage to a decimal value.
$$25\% =0.25$$Original\, price = \($\)19.50 / (1 -0.25)

STEP 9

Calculate the denominator.
$$-.25 =.75$$Original\, price = \($\)19.50 /.75

Calculate the original price.
Original\, price = \($\)19.50 /0.75 = \($\)26The original price of the book was $26.