Step by step
The question
Question: Adult tickets cost $8 and child tickets cost $5.
A cinema sold 4 times as many child tickets as adult tickets.
It made $560.
How many of each ticket did it sell?
1 Find what we know
What do we know?
Two kinds: adult tickets cost $8 each, child tickets cost $5 each.
There are 4 times as many child tickets as adult tickets.
All the money: $560.
What do we want?
How many adult tickets, and how many child tickets.
2 Name the unknown
We know the child tickets from the adult tickets.
So we start with the adult tickets.
We call how many there are x.
There are 4 times as many child tickets as adult tickets.
4 times x: 4x.
Careful!
There are 4 times as many child tickets as adult tickets.
So the child tickets are 4x, not the adult tickets.
The right way: 4x = child tickets.
Let's put it in a table: how many, the price, and the money.
Adult tickets: x of them, $8 each.
Child tickets: 4x of them, $5 each.
Money = how many times the price.
8 times x is 8x.
5 times 4x is 20x.
The total: $560 in all.
3 Write the equation
In words: the adult money plus the child money makes all the money.
So the equation is 8x + 20x = 560.
Now we solve it.
4 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.
8x + 20x = 28x.
Now we have 28x = 560.
Is x alone now?
Not yet: 28x means 28 times x.
How do we remove it?
5 Remove the 28
To remove times 28, we divide by 28.
We do it on both sides, so they stay equal.
28 divided by 28 is 1.
They cancel each other.
So just x is left.
560 divided by 28 is 20.
So x = 20.
6 Answer the question
Child tickets: 4x.
4 × 20 = 80.
So 20 adult tickets and 80 child tickets.
7 Check
Let's check in the story.
4 times 20 is 80: 4 times as many, like the story says.
The money: $160 plus $400 makes $560, like the story says.
Does it make sense?
Both are whole numbers, not below 0.
That fits 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.