Step by step
The question
Question: A town has 4,000 people.
The number grows 50%, then drops 50%.
How many people live there now?
1 Up 50% of 4,000
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.
4,000 divided by 10 is 400.
50% is 5 times 10%.
5 times 400 is 2,000.
Up 50% means we add 2,000.
4,000 plus 2,000 is 6,000.
2 Down 50% of 6,000
Now the number is 6,000.
The second 50% is not of the old number.
It is 50% of the new number, 6,000.
To find 10%, we divide by 10.
6,000 divided by 10 is 600.
50% is 5 times 10%.
5 times 600 is 3,000.
Down 50% means we take away 3,000.
6,000 minus 3,000 is 3,000.
Careful!
We can't just add the percents.
The second percent is of a new number.
You might think up 50% and down 50% cancel out.
But we did not get back to 4,000.
The second 50% is of 6,000, a bigger number.
So it is 3,000, not 2,000 like the first 50%.
So the new number is 3,000.
3 Check
Let's check another way: up 50% makes it 100% plus 50%.
That is 150% of the number.
150% is 150 out of 100: 1.5.
4,000 times 1.5 is 6,000.
Then: down 50% leaves 100% minus 50%.
That is 50% of the number.
50% is 50 out of 100: 0.5.
6,000 times 0.5 is 3,000.
The same.
So the answer is right!
Let's look back.
First: up 50% of 4,000.
Then: down 50% of 6,000.
Last: check.