Step by step
The question
Question: A town has 2,000 people.
The number grows 10%, then grows 10% again.
How many people live there now?
1 Up 10% of 2,000
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.
2,000 divided by 10 is 200.
Up 10% means we add 200.
2,000 plus 200 is 2,200.
2 Up 10% of 2,200
Now the number is 2,200.
The second 10% is not of the old number.
It is 10% of the new number, 2,200.
To find 10%, we divide by 10.
2,200 divided by 10 is 220.
Up 10% means we add 220.
2,200 plus 220 is 2,420.
Careful!
We can't just add the percents.
The second percent is of a new number.
So the new number is 2,420.
3 Check
Let's check another way: up 10% makes it 100% plus 10%.
That is 110% of the number.
110% is 110 out of 100: 1.1.
2,000 times 1.1 is 2,200.
Then: up 10% makes it 100% plus 10%.
That is 110% of the number.
110% is 110 out of 100: 1.1.
2,200 times 1.1 is 2,420.
The same.
So the answer is right!
Let's look back.
First: up 10% of 2,000.
Then: up 10% of 2,200.
Last: check.