Step by step
The question
Question: Tom got a 15% raise.
Now he earns $575 a week.
How much did he earn before the raise?
1 Find what we know
What do we know?
The pay goes up by 15%.
With the raise: $575.
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 15% of it.
15% means 15 out of 100.
What goes into 15 and 100?
We list the numbers that go into each.
Into 15: 1, 3, 5, 15.
Into 100: 1, 2, 4, 5, 10, 20, 25, 50, 100.
5 is the biggest one in both lists.
So that is 3 out of 20.
15% of x means 3/20 times x.
So the raise is 3x/20.
3 Write the equation
In words: the pay before, plus the raise, is the new pay.
So the equation is x + 3x/20 = 575.
Now we solve it.
4 Remove the fraction
The bottom number is 20.
A fraction means divide: 3x/20 is 3x divided by 20.
To remove divided by 20, we multiply by 20.
We multiply every part by 20, not only the fraction.
Each whole side is times 20, so x and 575 are times 20 too.
We do it on both sides, so they stay equal.
20 divided by 20 is 1.
The bottom is gone.
Is x alone now?
Not yet: x is still divided by 20.
How do we remove it?
We write it again, without the crossed-out parts.
20 times x is 20x.
20 times 575 is 11500.
No more fractions!
So after step 4: we multiplied by 20, and now we have 20x + 3x = 11500.
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.
20x + 3x = 23x.
Now we have 23x = 11500.
Is x alone now?
Not yet: 23x means 23 times x.
6 Remove the 23
To remove times 23, we divide by 23.
We do it on both sides, so they stay equal.
23 divided by 23 is 1.
They cancel each other.
So just x is left.
11500 divided by 23 is 500.
So x = 500.
7 Answer the question
So the pay before was $500.
8 Check
Let's check in the story.
The raise: 15% of $500.
$500 divided by 20 is $25.
Times 3 is $75.
$500 plus $75 is $575, like the story says.
Check it with the picture.
100% is $500.
15% of it is $75.
$500 plus $75 is $575.
Does it make sense?
The pay went up.
So the pay before, $500, is less than $575.
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.