Step by step
The question
Question: A plumber charges $40 plus $25 an hour.
The bill was $140.
How many hours was the job?
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Find what we know
What do we know?
$40 is paid one time.
$25 for each hour.
Altogether: $140.
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 25x + 40 = 140.
Now we solve it.
We want x by itself.
Two things are stuck to x: times 25 and + 40.
First x was times 25.
Then + 40.
To take them off, we go backwards.
First we remove the + 40.
Then the times 25.
4 Remove the + 40
To remove + 40, we take away 40.
We do it on both sides, so they stay equal.
+ 40 and − 40 make zero.
Cross them out.
140 − 40 = 100.
Now we have 25x = 100.
5 Remove the 25
25x means 25 times x.
We want just x.
To remove times 25, we divide by 25.
We do it on both sides, so they stay equal.
25 divided by 25 is 1.
So just x is left.
100 divided by 25 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 $25 each: 4 times 25 is $100.
Plus the $40 at the start: $140, like the story says.
Does it make sense?
A whole number of hours.
And the total, $140, is more than the $40 start.
So the answer is right!
8 Pick the choice
Our answer is 4 hours.
That is choice A.
9 Why not the others
B is 5.6.
Wrong: 140 ÷ 25: forgot the $40.
C is 7.2.
Wrong: added 40: 180 ÷ 25.
D is 100.
Wrong: 25x = 100, but we still had to divide by 25.
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.