Step by step
The question
Question: Adult tickets cost $15 and child tickets cost $10.
A museum sold 3 times as many adult tickets as child tickets.
It made $1100.
How many of each ticket did it sell?
1 Find what we know
What do we know?
Two kinds: adult tickets cost $15 each, child tickets cost $10 each.
There are 3 times as many adult tickets as child tickets.
All the money: $1100.
What do we want?
How many child tickets, and how many adult tickets.
2 Name the unknown
We know the adult tickets from the child tickets.
So we start with the child tickets.
We call how many there are x.
There are 3 times as many adult tickets as child tickets.
3 times x: 3x.
Careful!
There are 3 times as many adult tickets as child tickets.
So the adult tickets are 3x, not the child tickets.
Let's put it in a table: how many, the price, and the money.
Child tickets: x of them, $10 each.
Adult tickets: 3x of them, $15 each.
Money = how many times the price.
10 times x is 10x.
15 times all of 3x is 15(3x).
We keep 3x together in brackets.
The total: $1100 in all.
3 Write the equation
In words: the child money plus the adult money makes all the money.
So the equation is 10x + 15(3x) = 1100.
Now we solve it.
4 Open the brackets
The 15 in front of the bracket multiplies every part inside.
So we write 15 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.
10x + 45x = 55x.
Now we have 55x = 1100.
6 Remove the 55
55x means 55 times x.
We want just x.
To remove times 55, we divide by 55.
We do it on both sides, so they stay equal.
55 divided by 55 is 1.
So just x is left.
1100 divided by 55 is 20.
So x = 20!
7 Answer the question
Adult tickets: 3x.
3 × 20 = 60.
So 20 child tickets and 60 adult tickets.
8 Check
Let's check in the story.
3 times 20 is 60: 3 times as many, like the story says.
The money: $200 plus $900 makes $1100, 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.