Step by step
The question
Question: Ben can spend at most $20.
Each pen costs $1.50.
How many pens can he buy?
1 Find what we know
What do we know?
At most $20.
$1.50 for each pen.
What do we want?
How many pens.
2 Name the unknown
We don't know how many pens.
So we call it x.
At most $20 means $20 or less.
We write ≤ $20.
3 Write the inequality
In words: what the pens make is at most $20.
So the inequality is 1.5x ≤ 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 10.
We do it on both sides, so the sign stays true.
10 is a positive number, so the sign stays the same.
Times 10 moves the point 1 place to the right.
10 × 1.5x = 15x.
10 × 20 = 200.
Write the answers.
No more decimals!
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 the sign stays true.
15 divided by 15 is 1.
So just x is left.
We can make 200/15 simpler.
It is the same as 40/3.
So x is less than or equal to 40/3.
6 Show it on a number line
7 Answer the question
That is about 13.33.
Pens come in whole numbers.
The biggest whole number up to 13.33 is 13.
So we round down.
Careful!
At most means we may not go over.
So we always round down.
So at most 13 pens.
8 Check
Let's check in the story.
13 pens: $19.50.
That is not more than $20.
But 14 pens would be $21: too much.
So 13 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.