Step by step
The question
Question: A school has 500 students.
The number drops 20%, then grows 20%.
How many students are there now?
1 Down 20% of 500
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.
500 divided by 10 is 50.
20% is 2 times 10%.
2 times 50 is 100.
Down 20% means we take away 100.
500 minus 100 is 400.
2 Up 20% of 400
Now the number is 400.
The second 20% is not of the old number.
It is 20% of the new number, 400.
To find 10%, we divide by 10.
400 divided by 10 is 40.
20% is 2 times 10%.
2 times 40 is 80.
Up 20% means we add 80.
400 plus 80 is 480.
Careful!
We can't just add the percents.
The second percent is of a new number.
You might think down 20% and up 20% cancel out.
But we did not get back to 500.
The second 20% is of 400, a smaller number.
So it is 80, not 100 like the first 20%.
So the new number of students is 480.
3 Check
Let's check another way: down 20% leaves 100% minus 20%.
That is 80% of the number.
80% is 80 out of 100: 0.8.
500 times 0.8 is 400.
Then: up 20% makes it 100% plus 20%.
That is 120% of the number.
120% is 120 out of 100: 1.2.
400 times 1.2 is 480.
The same.
So the answer is right!
Let's look back.
First: down 20% of 500.
Then: up 20% of 400.
Last: check.