Step by step
The question
Question: Adult tickets cost $9 and child tickets cost $4.
A zoo sold twice as many child tickets as adult tickets.
It made $400.
How many of each ticket did it sell?
1 Find what we know
What do we know?
Two kinds: adult tickets cost $9 each, child tickets cost $4 each.
There are 2 times as many child tickets as adult tickets.
All the money: $400.
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 2 times as many child tickets as adult tickets.
2 times x: 2x.
Careful!
There are 2 times as many child tickets as adult tickets.
So the child 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.
Child tickets: 2x of them, $4 each.
Money = how many times the price.
9 times x is 9x.
4 times all of 2x is 4(2x).
We keep 2x together in brackets.
The total: $400 in all.
3 Write the equation
In words: the adult money plus the child money makes all the money.
So the equation is 9x + 4(2x) = 400.
Now we solve it.
4 Open the brackets
The 4 in front of the bracket multiplies every part inside.
So we write 4 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 + 8x = 17x.
Now we have 17x = 400.
6 Remove the 17
17x means 17 times x.
We want just x.
To remove times 17, we divide by 17.
We do it on both sides, so they stay equal.
17 divided by 17 is 1.
So just x is left.
So x = 400/17!
7 Answer the question
x = 400/17 is not a whole number.
There are no half tickets.
So there is no answer.
Let's look back.
First: find what we know.
Then: name the unknown.
Then: write the equation.
Then: solve it.
Last: answer the question.