Step by step
The question
Question: A phone plan costs $12 plus $0.25 each text.
Eva can pay at most $20.
How many texts can she send?
1 Find what we know
What do we know?
At most $20.
$0.25 for each text.
$12 one time.
What do we want?
How many texts.
2 Name the unknown
We don't know how many texts.
So we call it x.
At most $20 means $20 or less.
We write ≤ $20.
3 Write the inequality
In words: what the texts add, plus the start, is at most $20.
So the inequality is 0.25x + 12 ≤ 20.
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 100.
We do it on both sides, so the sign stays true.
100 is a positive number, so the sign stays the same.
Times 100 moves the point 2 places to the right.
100 × 0.25x = 25x.
100 × 12 = 1200.
100 × 20 = 2000.
Write the answers.
No more decimals!
We want x by itself.
Two things are stuck to x: times 25 and + 1200.
The + 1200 is on the outside, so it comes off first.
Then the times 25.
5 Remove the + 1200
To remove + 1200, we take away 1200.
We do it on both sides, so the sign stays true.
+ 1200 and − 1200 make zero.
Cross them out.
2000 − 1200 = 800.
Now we have 25x ≤ 800.
6 Remove the 25
25x means 25 times x.
We want just x.
To remove times 25, we divide by 25.
We do it on both sides, so the sign stays true.
25 divided by 25 is 1.
So just x is left.
800 divided by 25 is 32.
So x is less than or equal to 32.
7 Show it on a number line
8 Answer the question
Texts come in whole numbers.
32 is a whole number, so it stays.
Careful!
At most $20: exactly $20 is still OK.
So 32 texts is fine.
So at most 32 texts.
9 Check
Let's check in the story.
32 texts: $20.
That is not more than $20.
But 33 texts would be $20.25: too much.
So 32 is the most.
So the answer is right!
Let's look back.
First: find what we know.
Then: name the unknown.
Then: write the inequality.
Then: solve it.
Then: answer the question.
Last: check.