Step by step
The question
Question: A $80 jacket goes up 25%, then down 20%.
What is the new price?
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Up 25% of $80
Percent means out of 100.
So 10% is 10 out of 100.
That is the same as 1 out of 10: one tenth.
$80 divided by 10 is $8.
To find 10%, we divide by 10.
20% is 2 times 10%.
2 times $8 is $16.
5% is half of 10%.
Half of $8 is $4.
25% is 20% plus 5%.
$16 plus $4 is $20.
Up 25% means we add $20.
$80 plus $20 is $100.
2 Down 20% of $100
Now the price is $100.
The second 20% is not of the old number.
It is 20% of the new number, $100.
To find 10%, we divide by 10.
$100 divided by 10 is $10.
20% is 2 times 10%.
2 times $10 is $20.
Down 20% means we take away $20.
$100 minus $20 is $80.
Careful!
We can't just add the percents.
The second percent is of a new number.
So it is back to $80.
3 Check
Let's check another way: up 25% makes it 100% plus 25%.
That is 125% of the price.
125% is 125 out of 100: 1.25.
$80 times 1.25 is $100.
Then: down 20% leaves 100% minus 20%.
That is 80% of the price.
80% is 80 out of 100: 0.8.
$100 times 0.8 is $80.
The same.
So the answer is right!
4 Pick the choice
Our answer is $80.
That is choice B.
5 Why not the others
A is $64.
Wrong: took 20% off $80: forgot the 25% rise.
C is $84.
Wrong: 25% − 20% = 5% more: but the two percents are of different prices.
That is the Careful mistake from before.
D is $100.
Wrong: that is the price after the first change only.
Let's look back.
First: up 25% of $80.
Then: down 20% of $100.
Then: check.
Then: pick the choice.
Last: why not the others.