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Math

QuestionA desk is 35%35\% off and costs \$234. What is the original price?

Studdy Solution

STEP 1

Assumptions1. The sale price of the desk is $234. . The discount on the desk is35%.

STEP 2

We know that the sale price is the regular price minus the discount. We can express this as an equationSale price=Regular price−DiscountSale\, price = Regular\, price - Discount

STEP 3

We also know that the discount is the regular price times the discount rate. We can express this as another equationDiscount=Regular pricetimesDiscount rateDiscount = Regular\, price \\times Discount\, rate

STEP 4

Substituting the second equation into the first, we getSale price=Regular price−Regular pricetimesDiscount rateSale\, price = Regular\, price - Regular\, price \\times Discount\, rate

STEP 5

Rearranging the equation, we getRegular price=Sale price1−Discount rateRegular\, price = \frac{Sale\, price}{1 - Discount\, rate}

STEP 6

Now, plug in the given values for the sale price and discount rate to calculate the regular price.
Regular price=$2341−35%Regular\, price = \frac{\$234}{1 -35\%}

STEP 7

Convert the percentage to a decimal value.
35%=0.3535\% =0.35Regular price=$2341−0.35Regular\, price = \frac{\$234}{1 -0.35}

STEP 8

Calculate the denominator.
1−0.35=0.651 -0.35 =0.65Regular price=$2340.65Regular\, price = \frac{\$234}{0.65}

STEP 9

Calculate the regular price.
Regular price=$234.65=$360Regular\, price = \frac{\$234}{.65} = \$360The regular price of the desk is $360.

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