Step by step
The question
Question: A cinema sold 120 tickets.
Adult tickets cost $9 and child tickets cost $6.
The cinema made $930.
How many of each ticket were sold?
1 Find what we know
What do we know?
120 tickets in all.
Two kinds: adult tickets cost $9 each, child tickets cost $6 each.
All the money: $930.
What do we want?
How many adult tickets, and how many child tickets.
2 Name the unknown
We don't know how many adult tickets.
So we call it x.
The rest are child.
120 in all, take away the x adult ones: 120 − x.
For example: if 12 were adult, then 120 − 12 = 108 would be child.
So we need only one letter.
Let's put it in a table: how many, the price, and the money.
Adult: x tickets at $9 each.
Child: 120 − x tickets at $6 each.
Money = how many times the price.
9 times x is 9x.
6 times all of 120 − x is 6(120 − x).
We keep 120 − x together in brackets.
The total row: 120 tickets in all, and $930 in all.
3 Write the equation
In words: the adult money plus the child money makes all the money.
So the equation is 9x + 6(120 − x) = 930.
Now we solve it.
4 Open the brackets
The 6 in front of the bracket multiplies every part inside.
So we write 6 times each part.
Work out each multiplication.
5 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
All the x terms go together.
9x − 6x = 3x.
Now we have 3x + 720 = 930.
We want x by itself.
Two things are stuck to x: times 3 and + 720.
The + 720 is on the outside, so it comes off first.
Then the times 3.
6 Remove the + 720
To remove + 720, we take away 720.
We do it on both sides, so they stay equal.
+ 720 and − 720 make zero.
Cross them out.
930 − 720 = 210.
Now we have 3x = 210.
7 Remove the 3
3x means 3 times x.
We want just x.
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3 divided by 3 is 1.
So just x is left.
210 divided by 3 is 70.
So x = 70!
8 Answer the question
Child: 120 − x.
120 − 70 = 50.
So 70 adult tickets and 50 child tickets.
9 Check
Let's check in the story.
70 + 50 = 120 tickets, like the story says.
The money: $630 plus $300 makes $930, like the story says.
Does it make sense?
Both are whole numbers from 0 to 120.
That fits 120 tickets.
So the answer is right!
Let's look back.
First: find what we know.
Then: name the unknown.
Then: write the equation.
Then: solve it.
Then: answer the question.
Last: check.