Step by step
The question
Question: A gym costs $20 to join and $10 a month.
Tom paid $90.
How many months did he pay for?
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Find what we know
What do we know?
$20 is paid one time.
$10 for each month.
Altogether: $90.
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 10x + 20 = 90.
Now we solve it.
We want x by itself.
Two things are stuck to x: times 10 and + 20.
First x was times 10.
Then + 20.
To take them off, we go backwards.
First we remove the + 20.
Then the times 10.
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.
90 − 20 = 70.
Now we have 10x = 70.
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.
70 divided by 10 is 7.
So x = 7.
6 Answer the question
So the answer is 7 months.
7 Check
Let's check in the story.
7 months at $10 each: 7 times 10 is $70.
Plus the $20 at the start: $90, like the story says.
Does it make sense?
A whole number of months.
And the total, $90, is more than the $20 start.
So the answer is right!
8 Pick the choice
Our answer is 7 months.
That is choice A.
9 Why not the others
B is 9.
Wrong: 90 ÷ 10: forgot the $20.
C is 11.
Wrong: added 20: 110 ÷ 10.
D is 70.
Wrong: 10x = 70, but we still had to divide by 10.
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.