SOLUTION: the cost of the item is $56 after a 20% discount....what is original price? how do you get the answer?

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Question 396153: the cost of the item is $56 after a 20% discount....what is original price?
how do you get the answer?
Found 2 solutions by MathLover1, jim_thompson5910:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

20% off, she paid $56.
original price - 20% off=$56.
original price=x
20% off=(20/100)x

x-+%2820%2F100%29x=56
x-+%280.2%29x=56
x%281-+0.2%29=56
x%28+0.8%29=56
x+=56%2F0.8
x+=+70.........original price was $70

check:
20% off=(20/100)$70=0.2*$70=$14
original price - 20% off= $70 - $14 = $56.




Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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%2F0.8 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.