Step by step
The question
Question: A tutor charges $20 plus $15 an hour.
The bill was $80.
How many hours was the job?
1 Find what we know
What do we know?
$20 is paid one time.
$15 for each hour.
Altogether: $80.
What do we want?
How many hours.
2 Name the unknown
We don't know how many hours.
So we call it x.
3 Write the equation
In words: what the hours cost, plus the start, makes the total.
So the equation is 15x + 20 = 80.
Now we solve it.
We want x by itself.
First we remove the + 20, so 15x is alone.
Then we remove the times 15.
Is x alone now?
Not yet: + 20 is still with x.
How do we remove it?
4 Remove the + 20
To remove + 20, we take away 20.
We do it on both sides, so they stay equal.
+ 20 and − 20 cancel each other.
They make zero.
80 − 20 = 60.
Now we have 15x = 60.
So after step 4: we took away 20, and now we have 15x = 60.
Is x alone now?
Not yet: 15x means 15 times x.
5 Remove the 15
To remove times 15, we divide by 15.
We do it on both sides, so they stay equal.
15 divided by 15 is 1.
They cancel each other.
So just x is left.
60 divided by 15 is 4.
So x = 4.
6 Answer the question
So the answer is 4 hours.
7 Check
Let's check in the story.
4 hours at $15 each: 4 times 15 is $60.
Plus the $20 at the start: $80, like the story says.
Check it with the picture.
4 hours at $15 is $60.
With the $20, that makes $80.
Does it make sense?
A whole number of hours.
And the total, $80, is more than the $20 start.
So the answer is right!
8 Type it in
The answer box takes 5 characters.
4 has 1.
It fits.
We type 4.
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.