Step by step
The question
Question: Sam has $20.
He saves $15 each week.
He wants to have at least $100.
How many weeks must he save?
1 Find what we know
What do we know?
At least $100.
$15 for each week.
At the start: $20.
What do we want?
How many weeks.
2 Name the unknown
We don't know how many weeks.
So we call it x.
At least $100 means $100 or more.
We write ≥ $100.
3 Write the inequality
In words: what the weeks add, plus the start, is at least $100.
So the inequality is 15x + 20 ≥ 100.
Now we solve it.
We want x by itself.
Two things are stuck to x: times 15 and + 20.
The + 20 is on the outside, so it comes off first.
Then the times 15.
4 Remove the + 20
To remove + 20, we take away 20.
We do it on both sides, so the sign stays true.
+ 20 and − 20 make zero.
Cross them out.
100 − 20 = 80.
Now we have 15x ≥ 80.
5 Remove the 15
15x means 15 times x.
We want just x.
To remove times 15, we divide by 15.
We do it on both sides, so the sign stays true.
15 divided by 15 is 1.
So just x is left.
We can make 80/15 simpler.
It is the same as 16/3.
So x is greater than or equal to 16/3.
6 Show it on a number line
7 Answer the question
That is about 5.33.
Weeks come in whole numbers.
The smallest whole number from 5.33 up is 6.
So we round up.
Careful!
5.33 rounds to 5 the usual way.
But 5 weeks are $95.
That is not enough.
So we round up.
So at least 6 weeks.
8 Check
Let's check in the story.
6 weeks: $110.
That is at least $100.
But 5 weeks would be $95: not enough.
So 6 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.