Step by step
The question
Question: A $50 shirt goes up 20%, then down 20%.
What is the new price?
1 Up 20% of $50
Percent means out of 100.
So 10% is 10 out of 100.
That is the same as 1 out of 10: one tenth.
To find 10%, we divide by 10.
$50 divided by 10 is $5.
20% is 2 times 10%.
2 times $5 is $10.
Up 20% means we add $10.
$50 plus $10 is $60.
2 Down 20% of $60
Now the price is $60.
The second 20% is not of the old number.
It is 20% of the new number, $60.
To find 10%, we divide by 10.
$60 divided by 10 is $6.
20% is 2 times 10%.
2 times $6 is $12.
Down 20% means we take away $12.
$60 minus $12 is $48.
Careful!
We can't just add the percents.
The second percent is of a new number.
You might think up 20% and down 20% cancel out.
But we did not get back to $50.
The second 20% is of $60, a bigger number.
So it is $12, not $10 like the first 20%.
So the new price is $48.
3 Check
Let's check another way: up 20% makes it 100% plus 20%.
That is 120% of the price.
120% is 120 out of 100: 1.2.
$50 times 1.2 is $60.
Then: down 20% leaves 100% minus 20%.
That is 80% of the price.
80% is 80 out of 100: 0.8.
$60 times 0.8 is $48.
The same.
So the answer is right!
Let's look back.
First: up 20% of $50.
Then: down 20% of $60.
Last: check.