Step by step
The question
Question: In a sale, everything is 20% off.
A jacket costs $44 in the sale.
What was the price before the sale?
1 Find what we know
What do we know?
The price goes down by 20%.
In the sale, it costs $44.
What do we want?
The price before.
2 Name the unknown
We don't know the price before.
So we call it x.
The discount is 20% of it.
20% means 20 out of 100.
20 goes into 100: 20 × 5 = 100.
So 20 goes into both.
So that is 1 out of 5.
20% of x means 1/5 times x.
So the discount is x/5.
3 Write the equation
In words: the price before, take away the discount, is the sale price.
So the equation is x − x/5 = 44.
Now we solve it.
4 Remove the fraction
The bottom number is 5.
A fraction means divide: x/5 is x divided by 5.
To remove divided by 5, we multiply by 5.
We multiply every part by 5, not only the fraction.
Each whole side is times 5, so x and 44 are times 5 too.
We do it on both sides, so they stay equal.
5 divided by 5 is 1.
The bottom is gone.
Is x alone now?
Not yet: x is still divided by 5.
How do we remove it?
We write it again, without the crossed-out parts.
5 times x is 5x.
5 times 44 is 220.
No more fractions!
So after step 4: we multiplied by 5, and now we have 5x − x = 220.
5 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
All the x terms go together.
5x − x = 4x.
Now we have 4x = 220.
Is x alone now?
Not yet: 4x means 4 times x.
6 Remove the 4
To remove times 4, we divide by 4.
We do it on both sides, so they stay equal.
4 divided by 4 is 1.
They cancel each other.
So just x is left.
220 divided by 4 is 55.
So x = 55.
7 Answer the question
So the price before was $55.
8 Check
Let's check in the story.
The discount: 20% of $55.
$55 divided by 5 is $11.
$55 take away $11 is $44, like the story says.
Check it with the picture.
100% is $55.
20% of it is $11.
$55 take away $11 is $44.
Does it make sense?
The price went down.
So the price before, $55, is more than $44.
So the answer is right!
Let's look back.
First: find what we know.
Then: name the unknown.
Then: write the equation.
Then: solve it.
Then: answer the question.
Last: check.