Step by step
The question
Question: A phone plan costs $12 plus $0.50 per minute.
The bill was $27.
How many minutes were used?
1 Find what we know
What do we know?
$12 is paid one time.
$0.50 for each minute.
Altogether: $27.
What do we want?
How many minutes.
2 Name the unknown
We don't know how many minutes.
So we call it x.
3 Write the equation
In words: what the minutes cost, plus the start, makes the total.
So the equation is 0.5x + 12 = 27.
Now we solve it.
4 Remove the decimals
Decimals are hard to work with.
Let's get rid of them.
We multiply every part by 10.
We do it on both sides, so they stay equal.
Times 10 moves the point 1 place to the right.
10 × 0.5x = 5x.
10 × 12 = 120.
10 × 27 = 270.
Write the answers.
No more decimals!
We want x by itself.
Two things are stuck to x: times 5 and + 120.
The + 120 is on the outside, so it comes off first.
Then the times 5.
5 Remove the + 120
To remove + 120, we take away 120.
We do it on both sides, so they stay equal.
+ 120 and − 120 make zero.
Cross them out.
270 − 120 = 150.
Now we have 5x = 150.
6 Remove the 5
5x means 5 times x.
We want just x.
To remove times 5, we divide by 5.
We do it on both sides, so they stay equal.
5 divided by 5 is 1.
So just x is left.
150 divided by 5 is 30.
So x = 30!
7 Answer the question
So the answer is 30 minutes.
8 Check
Let's check in the story.
30 minutes at $0.50 each: 30 times 0.5 is $15.
Plus the $12 at the start: $27, like the story says.
Does it make sense?
A whole number of minutes.
And the total, $27, is more than the $12 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.