Step by step
The question
Question: A gym costs $20 to join and $15 a month.
Tom paid $95.
How many months did he pay for?
1 Find what we know
What do we know?
$20 is paid one time.
$15 for each month.
Altogether: $95.
What do we want?
How many months.
2 Name the unknown
We don't know how many months.
So we call it x.
3 Write the equation
In words: what the months cost, plus the start, makes the total.
So the equation is 15x + 20 = 95.
Now we solve it.
We want x by itself.
Two things are stuck to x: times 15 and + 20.
The + 20 is on the outside, so it comes off first.
Then the times 15.
4 Remove the + 20
To remove + 20, we take away 20.
We do it on both sides, so they stay equal.
+ 20 and − 20 make zero.
Cross them out.
95 − 20 = 75.
Now we have 15x = 75.
5 Remove the 15
15x means 15 times x.
We want just x.
To remove times 15, we divide by 15.
We do it on both sides, so they stay equal.
15 divided by 15 is 1.
So just x is left.
75 divided by 15 is 5.
So x = 5!
6 Answer the question
So the answer is 5 months.
7 Check
Let's check in the story.
5 months at $15 each: 5 times 15 is $75.
Plus the $20 at the start: $95, like the story says.
Does it make sense?
A whole number of months.
And the total, $95, is more than the $20 start.
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.