Question 230810
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.