Step by step
The question
Question: A $400 laptop goes down 25%, then up 25%.
What is the new price?
1 Down 25% of $400
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.
$400 divided by 10 is $40.
20% is 2 times 10%.
2 times $40 is $80.
5% is half of 10%.
Half of $40 is $20.
25% is 20% plus 5%.
$80 plus $20 is $100.
Down 25% means we take away $100.
$400 minus $100 is $300.
2 Up 25% of $300
Now the price is $300.
The second 25% is not of the old number.
It is 25% of the new number, $300.
To find 10%, we divide by 10.
$300 divided by 10 is $30.
20% is 2 times 10%.
2 times $30 is $60.
5% is half of 10%.
Half of $30 is $15.
25% is 20% plus 5%.
$60 plus $15 is $75.
Up 25% means we add $75.
$300 plus $75 is $375.
Careful!
We can't just add the percents.
The second percent is of a new number.
You might think down 25% and up 25% cancel out.
But we did not get back to $400.
The second 25% is of $300, a smaller number.
So it is $75, not $100 like the first 25%.
So the new price is $375.
3 Check
Let's check another way: down 25% leaves 100% minus 25%.
That is 75% of the price.
75% is 75 out of 100: 0.75.
$400 times 0.75 is $300.
Then: up 25% makes it 100% plus 25%.
That is 125% of the price.
125% is 125 out of 100: 1.25.
$300 times 1.25 is $375.
The same.
So the answer is right!
Let's look back.
First: down 25% of $400.
Then: up 25% of $300.
Last: check.