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QuestionJoachim bought shoes for \$40 after a 20% discount. What was the original price? a. \$8 b. \$50 c. \$45 d. \$100

Studdy Solution

STEP 1

Assumptions1. The final price of the shoes is $40. The discount on the shoes is20%
3. The discount is calculated on the original price

STEP 2

We know that the final price is the original price minus the discount. We can express this as an equationFinal price=Original price−DiscountFinal\, price = Original\, price - Discount

STEP 3

We also know that the discount is calculated as a percentage of the original price. We can express this asDiscount=Original pricetimesDiscount rateDiscount = Original\, price \\times Discount\, rate

STEP 4

Substitute the second equation into the first to getFinal price=Original price−Original pricetimesDiscount rateFinal\, price = Original\, price - Original\, price \\times Discount\, rate

STEP 5

Rearrange the equation to solve for the original priceOriginal price=Final price1−Discount rateOriginal\, price = \frac{Final\, price}{1 - Discount\, rate}

STEP 6

Now, plug in the given values for the final price and discount rate to calculate the original price.
Original price=$401−20%Original\, price = \frac{\$40}{1 -20\%}

STEP 7

Convert the percentage to a decimal value.
20%=0.220\% =0.2Original price=$401−0.2Original\, price = \frac{\$40}{1 -0.2}

STEP 8

Calculate the denominator.
1−0.2=0.81 -0.2 =0.8Original price=$400.8Original\, price = \frac{\$40}{0.8}

STEP 9

Calculate the original price.
Original price=$40.8=$50Original\, price = \frac{\$40}{.8} = \$50The original price of the shoes was $50.

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