Step by step
The question
Question: Front tickets cost $20 and back tickets cost $12.
A concert sold twice as many back tickets as front tickets.
It made $880.
How many of each ticket did it sell?
1 Find what we know
What do we know?
Two kinds: front tickets cost $20 each, back tickets cost $12 each.
There are 2 times as many back tickets as front tickets.
All the money: $880.
What do we want?
How many front tickets, and how many back tickets.
2 Name the unknown
We know the back tickets from the front tickets.
So we start with the front tickets.
We call how many there are x.
There are 2 times as many back tickets as front tickets.
2 times x: 2x.
Careful!
There are 2 times as many back tickets as front tickets.
So the back tickets are 2x, not the front tickets.
Let's put it in a table: how many, the price, and the money.
Front tickets: x of them, $20 each.
Back tickets: 2x of them, $12 each.
Money = how many times the price.
20 times x is 20x.
12 times all of 2x is 12(2x).
We keep 2x together in brackets.
The total: $880 in all.
3 Write the equation
In words: the front money plus the back money makes all the money.
So the equation is 20x + 12(2x) = 880.
Now we solve it.
4 Open the brackets
The 12 in front of the bracket multiplies every part inside.
So we write 12 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.
20x + 24x = 44x.
Now we have 44x = 880.
6 Remove the 44
44x means 44 times x.
We want just x.
To remove times 44, we divide by 44.
We do it on both sides, so they stay equal.
44 divided by 44 is 1.
So just x is left.
880 divided by 44 is 20.
So x = 20!
7 Answer the question
Back tickets: 2x.
2 × 20 = 40.
So 20 front tickets and 40 back tickets.
8 Check
Let's check in the story.
2 times 20 is 40: 2 times as many, like the story says.
The money: $400 plus $480 makes $880, 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.