Step by step
The question
Question: Student tickets cost $5 and adult tickets cost $9.
A school sold twice as many student tickets as adult tickets.
It made $570.
How many of each ticket did it sell?
1 Find what we know
What do we know?
Two kinds: student tickets cost $5 each, adult tickets cost $9 each.
There are 2 times as many student tickets as adult tickets.
All the money: $570.
What do we want?
How many adult tickets, and how many student tickets.
2 Name the unknown
We know the student tickets from the adult tickets.
So we start with the adult tickets.
We call how many there are x.
There are 2 times as many student tickets as adult tickets.
2 times x: 2x.
Careful!
There are 2 times as many student tickets as adult tickets.
So the student tickets are 2x, not the adult tickets.
Let's put it in a table: how many, the price, and the money.
Adult tickets: x of them, $9 each.
Student tickets: 2x of them, $5 each.
Money = how many times the price.
9 times x is 9x.
5 times all of 2x is 5(2x).
We keep 2x together in brackets.
The total: $570 in all.
3 Write the equation
In words: the adult money plus the student money makes all the money.
So the equation is 9x + 5(2x) = 570.
Now we solve it.
4 Open the brackets
The 5 in front of the bracket multiplies every part inside.
So we write 5 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 + 10x = 19x.
Now we have 19x = 570.
6 Remove the 19
19x means 19 times x.
We want just x.
To remove times 19, we divide by 19.
We do it on both sides, so they stay equal.
19 divided by 19 is 1.
So just x is left.
570 divided by 19 is 30.
So x = 30!
7 Answer the question
Student tickets: 2x.
2 × 30 = 60.
So 30 adult tickets and 60 student tickets.
8 Check
Let's check in the story.
2 times 30 is 60: 2 times as many, like the story says.
The money: $270 plus $300 makes $570, 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.