Step by step
The question
Question: A boat can carry at most 1000 kg.
Each crate weighs 120 kg.
How many crates can it carry?
1 Find what we know
What do we know?
At most 1000 kg.
120 kg for each crate.
What do we want?
How many crates.
2 Name the unknown
We don't know how many crates.
So we call it x.
At most 1000 kg means 1000 kg or less.
We write ≤ 1000 kg.
3 Write the inequality
In words: what the crates make is at most 1000 kg.
So the inequality is 120x ≤ 1000.
Now we solve it.
4 Remove the 120
120x means 120 times x.
We want just x.
To remove times 120, we divide by 120.
We do it on both sides, so the sign stays true.
120 divided by 120 is 1.
So just x is left.
We can make 1000/120 simpler.
It is the same as 25/3.
So x is less than or equal to 25/3.
5 Show it on a number line
6 Answer the question
That is about 8.33.
Crates come in whole numbers.
The biggest whole number up to 8.33 is 8.
So we round down.
Careful!
At most means we may not go over.
So we always round down.
So at most 8 crates.
7 Check
Let's check in the story.
8 crates: 960 kg.
That is not more than 1000 kg.
But 9 crates would be 1080 kg: too much.
So 8 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.