Step by step
The question
Question: Plan A costs $30 plus $2 per hour.
Plan B costs $10 plus $6 per hour.
After how many hours do the two plans cost the same?
1 Find what we know
What do we know?
Plan A: $30 one time, plus $2 for each hour.
Plan B: $10 one time, plus $6 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.
Plan A: $2 for each hour, so x hours cost 2x.
Plus $30 one time: 2x + 30.
Plan B: $6 for each hour, so x hours cost 6x.
Plus $10 one time: 6x + 10.
3 Write the equation
In words: Plan A's cost is the same as Plan B's cost.
So the equation is 2x + 30 = 6x + 10.
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 2x from the left side.
To remove 2x, we take away 2x.
We do it on both sides, so they stay equal.
2x and − 2x make zero.
Cross them out.
6x − 2x = 4x.
Now we have 30 = 4x + 10.
Let's swap the two sides, so x is on the left.
We want x by itself.
Two things are stuck to x: times 4 and + 10.
The + 10 is on the outside, so it comes off first.
Then the times 4.
5 Remove the + 10
To remove + 10, we take away 10.
We do it on both sides, so they stay equal.
+ 10 and − 10 make zero.
Cross them out.
30 − 10 = 20.
Now we have 4x = 20.
6 Remove the 4
4x means 4 times x.
We want just x.
To remove times 4, we divide by 4.
We do it on both sides, so they stay equal.
4 divided by 4 is 1.
So just x is left.
20 divided by 4 is 5.
So x = 5!
7 Answer the question
So after 5 hours, they cost the same.
8 Check
Let's check in the story.
Plan A: $30 + 5 × $2 = $40.
Plan B: $10 + 5 × $6 = $40.
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.