Step by step
The question
Question: A $100 bag goes up 20%, then up 20% again.
What is the total percent change?
1 Up 20% of $100
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.
$100 divided by 10 is $10.
20% is 2 times 10%.
2 times $10 is $20.
Up 20% means we add $20.
$100 plus $20 is $120.
2 Up 20% of $120
Now the price is $120.
The second 20% is not of the old number.
It is 20% of the new number, $120.
To find 10%, we divide by 10.
$120 divided by 10 is $12.
20% is 2 times 10%.
2 times $12 is $24.
Up 20% means we add $24.
$120 plus $24 is $144.
Careful!
We can't just add the percents.
The second percent is of a new number.
3 The total change
We started at $100 and ended at $144.
That is $44 more.
Percent means out of 100.
The percent change is the change over the start: 44 out of 100.
44 out of 100 is 44%.
So it is 44% more than at the start.
So the total change is 44% more.
4 Check
Let's check another way: up 20% makes it 100% plus 20%.
That is 120% of the price.
120% is 120 out of 100: 1.2.
$100 times 1.2 is $120.
Then: up 20% makes it 100% plus 20%.
That is 120% of the price.
120% is 120 out of 100: 1.2.
$120 times 1.2 is $144.
And 44% of $100 is $44.
$100 plus $44 is $144, the same end.
So the answer is right!
Let's look back.
First: up 20% of $100.
Then: up 20% of $120.
Then: the total change.
Last: check.