Step by step
The question
Question: A gym costs $25 to join plus $8 each visit.
Raj can spend at most $100.
How many visits can he make?
1 Find what we know
What do we know?
At most $100.
$8 for each visit.
$25 one time.
What do we want?
How many visits.
2 Name the unknown
We don't know how many visits.
So we call it x.
At most $100 means $100 or less.
We write ≤ $100.
3 Write the inequality
In words: what the visits add, plus the start, is at most $100.
So the inequality is 8x + 25 ≤ 100.
Now we solve it.
We want x by itself.
Two things are stuck to x: times 8 and + 25.
The + 25 is on the outside, so it comes off first.
Then the times 8.
4 Remove the + 25
To remove + 25, we take away 25.
We do it on both sides, so the sign stays true.
+ 25 and − 25 make zero.
Cross them out.
100 − 25 = 75.
Now we have 8x ≤ 75.
5 Remove the 8
8x means 8 times x.
We want just x.
To remove times 8, we divide by 8.
We do it on both sides, so the sign stays true.
8 divided by 8 is 1.
So just x is left.
So x is less than or equal to 75/8.
6 Show it on a number line
7 Answer the question
That is about 9.38.
Visits come in whole numbers.
The biggest whole number up to 9.38 is 9.
So we round down.
Careful!
At most means we may not go over.
So we always round down.
So at most 9 visits.
8 Check
Let's check in the story.
9 visits: $97.
That is not more than $100.
But 10 visits would be $105: too much.
So 9 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.