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

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(20849) (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

.........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) (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 . 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 and set this equal to the known discount price of 56

Start with the given equation.

Subtract

Divide both sides by 0.8 to isolate x.

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.
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