QuestionWhat was the original price of a book that Kyle bought for \$ 19.50 after a 25% discount?

Studdy Solution

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.
$-.25 =.75$ $Original\, price = \$19.50 /.75$

STEP 10

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

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