Step by step
The question
Question: A $40 game goes up 50%, then down 50%.
What is the new price?
1 Up 50% of $40
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.
$40 divided by 10 is $4.
50% is 5 times 10%.
5 times $4 is $20.
Up 50% means we add $20.
$40 plus $20 is $60.
2 Down 50% of $60
Now the price is $60.
The second 50% is not of the old number.
It is 50% of the new number, $60.
To find 10%, we divide by 10.
$60 divided by 10 is $6.
50% is 5 times 10%.
5 times $6 is $30.
Down 50% means we take away $30.
$60 minus $30 is $30.
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 $40.
The second 50% is of $60, a bigger number.
So it is $30, not $20 like the first 50%.
So the new price is $30.
3 Check
Let's check another way: up 50% makes it 100% plus 50%.
That is 150% of the price.
150% is 150 out of 100: 1.5.
$40 times 1.5 is $60.
Then: down 50% leaves 100% minus 50%.
That is 50% of the price.
50% is 50 out of 100: 0.5.
$60 times 0.5 is $30.
The same.
So the answer is right!
Let's look back.
First: up 50% of $40.
Then: down 50% of $60.
Last: check.