Step by step
The question
Question: Ana got a 10% raise.
Now she earns $550 a week.
How much did she earn before the raise?
1 Find what we know
What do we know?
The pay goes up by 10%.
With the raise: $550.
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 10% of it.
10% means 10 out of 100.
That is 1 out of 10.
So the raise is x divided by 10: x/10.
3 Write the equation
In words: the pay before, plus the raise, is the new pay.
So the equation is x + x/10 = 550.
Now we solve it.
4 Remove the fraction
The bottom number is 10.
Times 10 will remove it.
We multiply every part by 10.
We do it on both sides, so they stay equal.
10 divided by 10 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.
10x + x = 11x.
Now we have 11x = 5500.
6 Remove the 11
11x means 11 times x.
We want just x.
To remove times 11, we divide by 11.
We do it on both sides, so they stay equal.
11 divided by 11 is 1.
So just x is left.
5500 divided by 11 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: 10% of $500.
$500 divided by 10 is $50.
$500 plus $50 is $550, like the story says.
Does it make sense?
The pay went up.
So the pay before, $500, is less than $550.
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.