Question 396153
Unfortunately the first answer is incorrect. Why? Because a 20% discount subtracts 20% of the original price from the original price. It's not simply 20% of the original price. This is a common pitfall with these types of problems.



Let x = original price.


Since "the cost of the item is $56 after a 20% discount", this means that {{{x-0.2x=56}}}. Basically, the original price is x and 20% of this price is 0.2x. Subtract 0.2x from x to get the discount price of {{{x-0.2x}}} and set this equal to the known discount price of 56



{{{x-0.2x=56}}} Start with the given equation.



{{{0.8x=56}}} Subtract



{{{x=56/0.8}}} Divide both sides by 0.8 to isolate x.



{{{x=70}}} Divide.



So the original price is 70 dollars.



Check: 



Notice that 20% of 70 dollars is 0.2*70 = 14 dollars



So subtract 14 dollars from 70 dollars to get: 70 - 14 = 56



So this confirms our answer.