Step by step
The question
Question: A lift can carry at most 600 kg.
Each box weighs 80 kg.
How many boxes can it carry?
1 Find what we know
What do we know?
At most 600 kg.
80 kg for each box.
What do we want?
How many boxes.
2 Name the unknown
We don't know how many boxes.
So we call it x.
At most 600 kg means 600 kg or less.
We write ≤ 600 kg.
3 Write the inequality
In words: what the boxes make is at most 600 kg.
So the inequality is 80x ≤ 600.
Now we solve it.
4 Remove the 80
80x means 80 times x.
We want just x.
To remove times 80, we divide by 80.
We do it on both sides, so the sign stays true.
80 divided by 80 is 1.
So just x is left.
We can make 600/80 simpler.
It is the same as 15/2.
So x is less than or equal to 15/2.
5 Show it on a number line
6 Answer the question
15/2 is 7.5.
Boxes come in whole numbers.
The biggest whole number up to 7.5 is 7.
So we round down.
Careful!
7.5 rounds to 8 the usual way.
But 8 boxes are 640 kg.
That is too much.
So we round down.
So at most 7 boxes.
7 Check
Let's check in the story.
7 boxes: 560 kg.
That is not more than 600 kg.
But 8 boxes would be 640 kg: too much.
So 7 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.