# The price of a pair of trousers was decreased by 22% to $30. What was the original price of the trousers?

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### 2 Answers

We will assume that the original price before price reduction = x

The price was decreased by 22%

Then the price after sale = The original [price - the amount reduced

= x - (22% x) = 30

But given that the vurrent price ( after reductions) = $ 30

Then we will write:

x - 22%*x = 30

But 22% = 22/100 = 0.22

==> x - 0.22 x = 30

==> 0.78 x = 30

Now we will divide by 0.78

==> x = 30/ 0.78 = 38.46 ( approx.)

**Then the original price of the trousers was = $ 38.46**

Here the 30 dollar is the result after decreasing the 22% discount from the original price.

So if the original price is 100%, after decreasing the 22% , the resulting price should be (100-22)% = 78% of the original price.

So the question is if 88%of the original price is $30, then what should be the original price.

We can now easily see that $30 should be multiplied by 100/78.

So the original price should be 30*100/88 = $38.76