Step by step
The question
Question: Tom has $15.
He earns $9 each hour.
He wants at least $100.
How many hours must he work?
1 Find what we know
What do we know?
At least $100.
$9 for each hour.
At the start: $15.
What do we want?
How many hours.
2 Name the unknown
We don't know how many hours.
So we call it x.
At least $100 means $100 or more.
We write ≥ $100.
3 Write the inequality
In words: what the hours add, plus the start, is at least $100.
So the inequality is 9x + 15 ≥ 100.
Now we solve it.
We want x by itself.
Two things are stuck to x: times 9 and + 15.
The + 15 is on the outside, so it comes off first.
Then the times 9.
4 Remove the + 15
To remove + 15, we take away 15.
We do it on both sides, so the sign stays true.
+ 15 and − 15 make zero.
Cross them out.
100 − 15 = 85.
Now we have 9x ≥ 85.
5 Remove the 9
9x means 9 times x.
We want just x.
To remove times 9, we divide by 9.
We do it on both sides, so the sign stays true.
9 divided by 9 is 1.
So just x is left.
So x is greater than or equal to 85/9.
6 Show it on a number line
7 Answer the question
That is about 9.44.
Hours come in whole numbers.
The smallest whole number from 9.44 up is 10.
So we round up.
Careful!
9.44 rounds to 9 the usual way.
But 9 hours are $96.
That is not enough.
So we round up.
So at least 10 hours.
8 Check
Let's check in the story.
10 hours: $105.
That is at least $100.
But 9 hours would be $96: not enough.
So 10 is the fewest.
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.