Step by step
The question
Question: A van can carry no more than 900 kg.
Each bag weighs 50 kg.
How many bags can it carry?
1 Find what we know
What do we know?
No more than 900 kg.
50 kg for each bag.
What do we want?
How many bags.
2 Name the unknown
We don't know how many bags.
So we call it x.
No more than 900 kg means 900 kg or less.
We write ≤ 900 kg.
3 Write the inequality
In words: what the bags make is no more than 900 kg.
So the inequality is 50x ≤ 900.
Now we solve it.
4 Remove the 50
50x means 50 times x.
We want just x.
To remove times 50, we divide by 50.
We do it on both sides, so the sign stays true.
50 divided by 50 is 1.
So just x is left.
900 divided by 50 is 18.
So x is less than or equal to 18.
5 Show it on a number line
6 Answer the question
Bags come in whole numbers.
18 is a whole number, so it stays.
Careful!
No more than 900 kg: exactly 900 kg is still OK.
So 18 bags is fine.
So at most 18 bags.
7 Check
Let's check in the story.
18 bags: 900 kg.
That is not more than 900 kg.
But 19 bags would be 950 kg: too much.
So 18 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.