Step by step
The question
Question: Gym A charges $20 plus $5 per visit.
Gym B charges $9 per visit.
After how many visits do the two gyms cost the same?
1 Find what we know
What do we know?
Gym A: $20 one time, plus $5 for each visit.
Gym B: $9 for each visit.
What do we want?
How many visits make the two costs the same.
2 Name the unknown
We don't know how many visits.
So we call it x.
Gym A: $5 for each visit, so x visits cost 5x.
Plus $20 one time: 5x + 20.
Gym B: $9 for each visit, so x visits cost 9x.
3 Write the equation
In words: Gym A's cost is the same as Gym B's cost.
So the equation is 5x + 20 = 9x.
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 5x from the left side.
To remove 5x, we take away 5x.
We do it on both sides, so they stay equal.
5x and − 5x make zero.
Cross them out.
9x − 5x = 4x.
Now we have 20 = 4x.
Let's swap the two sides, so x is on the left.
5 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!
6 Answer the question
So after 5 visits, they cost the same.
7 Check
Let's check in the story.
Gym A: $20 + 5 × $5 = $45.
Gym B: 5 × $9 = $45.
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.