Step by step
The question
Question: A $250 bike goes up 20%, then down 10%.
What is the new price?
1 Up 20% of $250
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.
$250 divided by 10 is $25.
20% is 2 times 10%.
2 times $25 is $50.
Up 20% means we add $50.
$250 plus $50 is $300.
2 Down 10% of $300
Now the price is $300.
The second 10% is not of the old number.
It is 10% of the new number, $300.
To find 10%, we divide by 10.
$300 divided by 10 is $30.
Down 10% means we take away $30.
$300 minus $30 is $270.
Careful!
We can't just add the percents.
The second percent is of a new number.
So the new price is $270.
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.
$250 times 1.2 is $300.
Then: down 10% leaves 100% minus 10%.
That is 90% of the price.
90% is 90 out of 100: 0.9.
$300 times 0.9 is $270.
The same.
So the answer is right!
Let's look back.
First: up 20% of $250.
Then: down 10% of $300.
Last: check.