SOLUTION: The sale price of a radio is 30% below the original price of the radio, but a 7% sales tax is added to the sale price. Rob’s total bill for his radio came to $97.54. What was the o

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The sale price of a radio is 30% below the original price of the radio, but a 7% sales tax is added to the sale price. Rob’s total bill for his radio came to $97.54. What was the o      Log On


   

Question 230810: The sale price of a radio is 30% below the original price of the radio, but a 7% sales tax is added to the sale price. Rob’s total bill for his radio came to $97.54. What was the original price of the radio Rob bought on sale?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
sale price = .7 * original price.

7% tax is added to the sale price.

total bill came to $97.54

This means that .7 * original price + .07 * .7 * original price = 97.54

let x = original price.

this formula becomes:

.7*x + .07*.7*x = $97.54

factor out the x to get:

(.7 + .07*.7) * x = $97.54

simplify and combine like terms to get:

.749 * x = $97.54

divide both sides of equation by .749 to get:

x = 97.54 / .749

simplify to get:

x = 130.2269693

original price of the radio is $130.2269693

this is not an even number, but it works.

take 30% off that to get a sale price of $91.1588785

Add 7% sales tax to that to get a total bill of $97.54

Normally these types of problems will get you an even number for the original price but this one doesn't.

Despite that, the method looks good and so I believe this must be the answer you are looking for.