Step by step
The question
Question: Mia can spend no more than $50.
The bus costs $6.
Tickets cost $8 each.
How many tickets can she buy?
1 Find what we know
What do we know?
No more than $50.
$8 for each ticket.
$6 one time.
What do we want?
How many tickets.
2 Name the unknown
We don't know how many tickets.
So we call it x.
No more than $50 means $50 or less.
We write ≤ $50.
3 Write the inequality
In words: what the tickets add, plus the start, is no more than $50.
So the inequality is 8x + 6 ≤ 50.
Now we solve it.
We want x by itself.
Two things are stuck to x: times 8 and + 6.
The + 6 is on the outside, so it comes off first.
Then the times 8.
4 Remove the + 6
To remove + 6, we take away 6.
We do it on both sides, so the sign stays true.
+ 6 and − 6 make zero.
Cross them out.
50 − 6 = 44.
Now we have 8x ≤ 44.
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.
We can make 44/8 simpler.
It is the same as 11/2.
So x is less than or equal to 11/2.
6 Show it on a number line
7 Answer the question
11/2 is 5.5.
Tickets come in whole numbers.
The biggest whole number up to 5.5 is 5.
So we round down.
Careful!
5.5 rounds to 6 the usual way.
But 6 tickets are $54.
That is too much.
So we round down.
So at most 5 tickets.
8 Check
Let's check in the story.
5 tickets: $46.
That is not more than $50.
But 6 tickets would be $54: too much.
So 5 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.