Step by step
The question
Question: A school sold 200 tickets.
Adult tickets cost $5 and child tickets cost $3.
The school made $760.
How many of each ticket were sold?
1 Find what we know
What do we know?
200 tickets in all.
Two kinds: adult tickets cost $5 each, child tickets cost $3 each.
All the money: $760.
What do we want?
How many adult tickets, and how many child tickets.
2 Name the unknown
We don't know how many adult tickets.
So we call it x.
The rest are child.
200 in all, take away the x adult ones: 200 − x.
For example: if 20 were adult, then 200 − 20 = 180 would be child.
So we need only one letter.
Let's put it in a table: how many, the price, and the money.
Adult: x tickets at $5 each.
Child: 200 − x tickets at $3 each.
Money = how many times the price.
5 times x is 5x.
3 times all of 200 − x is 3(200 − x).
We keep 200 − x together in brackets.
The total row: 200 tickets in all, and $760 in all.
3 Write the equation
In words: the adult money plus the child money makes all the money.
So the equation is 5x + 3(200 − x) = 760.
Now we solve it.
4 Open the brackets
The 3 in front of the bracket multiplies every part inside.
So we write 3 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.
5x − 3x = 2x.
Now we have 2x + 600 = 760.
We want x by itself.
Two things are stuck to x: times 2 and + 600.
The + 600 is on the outside, so it comes off first.
Then the times 2.
6 Remove the + 600
To remove + 600, we take away 600.
We do it on both sides, so they stay equal.
+ 600 and − 600 make zero.
Cross them out.
760 − 600 = 160.
Now we have 2x = 160.
7 Remove the 2
2x means 2 times x.
We want just x.
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2 divided by 2 is 1.
So just x is left.
160 divided by 2 is 80.
So x = 80!
8 Answer the question
Child: 200 − x.
200 − 80 = 120.
So 80 adult tickets and 120 child tickets.
9 Check
Let's check in the story.
80 + 120 = 200 tickets, like the story says.
The money: $400 plus $360 makes $760, like the story says.
Does it make sense?
Both are whole numbers from 0 to 200.
That fits 200 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.