Step by step
The question
Question: A dog walker charges $8 plus $6 per hour.
A walk costs $38.
How many hours was the walk?
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Find what we know
What do we know?
$8 is paid one time.
$6 for each hour.
Altogether: $38.
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 6x + 8 = 38.
Now we solve it.
We want x by itself.
First we remove the + 8, so 6x is alone.
Then we remove the times 6.
Is x alone now?
Not yet: + 8 is still with x.
How do we remove it?
4 Remove the + 8
To remove + 8, we take away 8.
We do it on both sides, so they stay equal.
+ 8 and − 8 cancel each other.
They make zero.
38 − 8 = 30.
Now we have 6x = 30.
So after step 4: we took away 8, and now we have 6x = 30.
Is x alone now?
Not yet: 6x means 6 times x.
5 Remove the 6
To remove times 6, we divide by 6.
We do it on both sides, so they stay equal.
6 divided by 6 is 1.
They cancel each other.
So just x is left.
30 divided by 6 is 5.
So x = 5.
6 Answer the question
So the answer is 5 hours.
7 Check
Let's check in the story.
5 hours at $6 each: 5 times 6 is $30.
Plus the $8 at the start: $38, like the story says.
Check it with the picture.
5 hours at $6 is $30.
With the $8, that makes $38.
Does it make sense?
A whole number of hours.
And the total, $38, is more than the $8 start.
So the answer is right!
8 Pick the choice
Our answer is 5 hours.
That is choice A.
9 Why not the others
B is 19/3.
Wrong: 38 ÷ 6: forgot the $8.
C is 23/3.
Wrong: added 8: 46 ÷ 6.
D is 30.
Wrong: 6x = 30, but we still had to divide by 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.