Step by step
The question
Question: In a sale, everything is 20% off.
A coat costs $40 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 $40.
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.
That is 1 out of 5.
So the discount is x divided by 5: 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 = 40.
Now we solve it.
4 Remove the fraction
The bottom number is 5.
Times 5 will remove it.
We multiply every part by 5.
We do it on both sides, so they stay equal.
5 divided by 5 is 1.
Write what is left.
Do the multiplications.
No more fractions!
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 = 200.
6 Remove the 4
4x means 4 times x.
We want just x.
To remove times 4, we divide by 4.
We do it on both sides, so they stay equal.
4 divided by 4 is 1.
So just x is left.
200 divided by 4 is 50.
So x = 50!
7 Answer the question
So the price before was $50.
8 Check
Let's check in the story.
The discount: 20% of $50.
$50 divided by 5 is $10.
$50 take away $10 is $40, like the story says.
Does it make sense?
The price went down.
So the price before, $50, is more than $40.
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.