Step by step
The question
Question: Mia can spend at most $40.
Each book costs $6.
How many books can she buy?
1 Find what we know
What do we know?
At most $40.
$6 for each book.
What do we want?
How many books.
2 Name the unknown
We don't know how many books.
So we call it x.
At most $40 means $40 or less.
We write ≤ $40.
3 Write the inequality
In words: what the books make is at most $40.
So the inequality is 6x ≤ 40.
Now we solve it.
4 Remove the 6
6x means 6 times x.
We want just x.
To remove times 6, we divide by 6.
We do it on both sides, so the sign stays true.
6 divided by 6 is 1.
So just x is left.
We can make 40/6 simpler.
It is the same as 20/3.
So x is less than or equal to 20/3.
5 Show it on a number line
6 Answer the question
That is about 6.67.
Books come in whole numbers.
The biggest whole number up to 6.67 is 6.
So we round down.
Careful!
6.67 rounds to 7 the usual way.
But 7 books are $42.
That is too much.
So we round down.
So at most 6 books.
7 Check
Let's check in the story.
6 books: $36.
That is not more than $40.
But 7 books would be $42: too much.
So 6 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.