Step by step
The question
Question: A bike rental costs $10 plus $4 per hour.
Mia paid $34.
How many hours did she rent the bike?
1 Find what we know
What do we know?
$10 is paid one time.
$4 for each hour.
Altogether: $34.
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 4x + 10 = 34.
Now we solve it.
We want x by itself.
First we remove the + 10, so 4x is alone.
Then we remove the times 4.
Is x alone now?
Not yet: + 10 is still with x.
How do we remove it?
4 Remove the + 10
To remove + 10, we take away 10.
We do it on both sides, so they stay equal.
+ 10 and − 10 cancel each other.
They make zero.
34 − 10 = 24.
Now we have 4x = 24.
So after step 4: we took away 10, and now we have 4x = 24.
Is x alone now?
Not yet: 4x means 4 times x.
5 Remove the 4
To remove times 4, we divide by 4.
We do it on both sides, so they stay equal.
4 divided by 4 is 1.
They cancel each other.
So just x is left.
24 divided by 4 is 6.
So x = 6.
6 Answer the question
So the answer is 6 hours.
7 Check
Let's check in the story.
6 hours at $4 each: 6 times 4 is $24.
Plus the $10 at the start: $34, like the story says.
Check it with the picture.
6 hours at $4 is $24.
With the $10, that makes $34.
Does it make sense?
A whole number of hours.
And the total, $34, is more than the $10 start.
So the answer is right!
8 Type it in
The answer box takes 5 characters.
6 has 1.
It fits.
We type 6.
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.