Step by step
The question
Question: A bike costs $200.
The price goes up 10%, then goes up 10% again.
What is the new price?
1 Up 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.
To find 10%, we divide by 10.
$200 divided by 10 is $20.
Up 10% means we add $20.
$200 plus $20 is $220.
2 Up 10% of $220
Now the price is $220.
The second 10% is not of the old number.
It is 10% of the new number, $220.
To find 10%, we divide by 10.
$220 divided by 10 is $22.
Up 10% means we add $22.
$220 plus $22 is $242.
Careful!
We can't just add the percents.
The second percent is of a new number.
So the new price is $242.
3 Check
Let's check another way: up 10% makes it 100% plus 10%.
That is 110% of the price.
110% is 110 out of 100: 1.1.
$200 times 1.1 is $220.
Then: up 10% makes it 100% plus 10%.
That is 110% of the price.
110% is 110 out of 100: 1.1.
$220 times 1.1 is $242.
The same.
So the answer is right!
Let's look back.
First: up 10% of $200.
Then: up 10% of $220.
Last: check.