Step by step
The question
Question: A $200 bag goes down 10%, then up 10%.
What is the new price?
1 Down 10% of $200
Percent means out of 100.
So 10% is 10 out of 100.
That is the same as 1 out of 10: one tenth.
$200 divided by 10 is $20.
To find 10%, we divide by 10.
Down 10% means we take away $20.
$200 minus $20 is $180.
2 Up 10% of $180
Now the price is $180.
The second 10% is not of the old number.
It is 10% of the new number, $180.
To find 10%, we divide by 10.
$180 divided by 10 is $18.
Up 10% means we add $18.
$180 plus $18 is $198.
Careful!
We can't just add the percents.
The second percent is of a new number.
So the new price is $198.
3 Check
Let's check another way: down 10% leaves 100% minus 10%.
That is 90% of the price.
90% is 90 out of 100: 0.9.
$200 times 0.9 is $180.
Then: up 10% makes it 100% plus 10%.
That is 110% of the price.
110% is 110 out of 100: 1.1.
$180 times 1.1 is $198.
The same.
So the answer is right!
Let's look back.
First: down 10% of $200.
Then: up 10% of $180.
Last: check.