Step by step
The question
Question: Plumber A charges $40 plus $20 per hour.
Plumber B charges $30 per hour.
After how many hours do they cost the same?
1 Find what we know
What do we know?
Plumber A: $40 one time, plus $20 for each hour.
Plumber B: $30 for each hour.
What do we want?
How many hours make the two costs the same.
2 Name the unknown
We don't know how many hours.
So we call it x.
Plumber A: $20 for each hour, so x hours cost 20x.
Plus $40 one time: 20x + 40.
Plumber B: $30 for each hour, so x hours cost 30x.
3 Write the equation
In words: Plumber A's cost is the same as Plumber B's cost.
So the equation is 20x + 40 = 30x.
Now we solve it.
4 Get x on one side
There is x on both sides.
We want x on one side only.
So we remove the 20x from the left side.
To remove 20x, we take away 20x.
We do it on both sides, so they stay equal.
20x and − 20x make zero.
Cross them out.
30x − 20x = 10x.
Now we have 40 = 10x.
Let's swap the two sides, so x is on the left.
5 Remove the 10
10x means 10 times x.
We want just x.
To remove times 10, we divide by 10.
We do it on both sides, so they stay equal.
10 divided by 10 is 1.
So just x is left.
40 divided by 10 is 4.
So x = 4!
6 Answer the question
So after 4 hours, they cost the same.
7 Check
Let's check in the story.
Plumber A: $40 + 4 × $20 = $120.
Plumber B: 4 × $30 = $120.
The same cost, like the story says.
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.