Step by step
The question
Question: Sami got a 12% raise.
Now he earns $33600 a year.
How much did he earn before the raise?
1 Find what we know
What do we know?
The pay goes up by 12%.
With the raise: $33600.
What do we want?
The pay before.
2 Name the unknown
We don't know the pay before.
So we call it x.
The raise is 12% of it.
12% means 12 out of 100.
What goes into 12 and 100?
We list the numbers that go into each.
Into 12: 1, 2, 3, 4, 6, 12.
Into 100: 1, 2, 4, 5, 10, 20, 25, 50, 100.
4 is the biggest one in both lists.
So that is 3 out of 25.
12% of x means 3/25 times x.
So the raise is 3x/25.
3 Write the equation
In words: the pay before, plus the raise, is the new pay.
So the equation is x + 3x/25 = 33600.
Now we solve it.
4 Remove the fraction
The bottom number is 25.
A fraction means divide: 3x/25 is 3x divided by 25.
To remove divided by 25, we multiply by 25.
We multiply every part by 25, not only the fraction.
Each whole side is times 25, so x and 33600 are times 25 too.
We do it on both sides, so they stay equal.
25 divided by 25 is 1.
The bottom is gone.
Is x alone now?
Not yet: x is still divided by 25.
How do we remove it?
We write it again, without the crossed-out parts.
25 times x is 25x.
25 times 33600 is 840000.
No more fractions!
So after step 4: we multiplied by 25, and now we have 25x + 3x = 840000.
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.
25x + 3x = 28x.
Now we have 28x = 840000.
Is x alone now?
Not yet: 28x means 28 times x.
6 Remove the 28
To remove times 28, we divide by 28.
We do it on both sides, so they stay equal.
28 divided by 28 is 1.
They cancel each other.
So just x is left.
840000 divided by 28 is 30000.
So x = 30000.
7 Answer the question
So the pay before was $30000.
8 Check
Let's check in the story.
The raise: 12% of $30000.
$30000 divided by 25 is $1200.
Times 3 is $3600.
$30000 plus $3600 is $33600, like the story says.
Check it with the picture.
100% is $30000.
12% of it is $3600.
$30000 plus $3600 is $33600.
Does it make sense?
The pay went up.
So the pay before, $30000, is less than $33600.
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.