Step by step
The question
Question: Adult tickets cost $25 and child tickets cost $15.
A circus sold 30 more child tickets than adult tickets.
It made $2450.
How many of each ticket did it sell?
1 Find what we know
What do we know?
Two kinds: adult tickets cost $25 each, child tickets cost $15 each.
There are 30 more child tickets than adult tickets.
All the money: $2450.
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.
30 more: x + 30.
Careful!
There are 30 more child tickets than adult tickets.
So the + 30 goes with the child tickets, not the adult tickets.
Let's put it in a table: how many, the price, and the money.
Adult tickets: x of them, $25 each.
Child tickets: x + 30 of them, $15 each.
Money = how many times the price.
25 times x is 25x.
15 times all of x + 30 is 15(x + 30).
We keep x + 30 together in brackets.
The total: $2450 in all.
3 Write the equation
In words: the adult money plus the child money makes all the money.
So the equation is 25x + 15(x + 30) = 2450.
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.
25x + 15x = 40x.
Now we have 40x + 450 = 2450.
We want x by itself.
Two things are stuck to x: times 40 and + 450.
The + 450 is on the outside, so it comes off first.
Then the times 40.
6 Remove the + 450
To remove + 450, we take away 450.
We do it on both sides, so they stay equal.
+ 450 and − 450 make zero.
Cross them out.
2450 − 450 = 2000.
Now we have 40x = 2000.
7 Remove the 40
40x means 40 times x.
We want just x.
To remove times 40, we divide by 40.
We do it on both sides, so they stay equal.
40 divided by 40 is 1.
So just x is left.
2000 divided by 40 is 50.
So x = 50!
8 Answer the question
Child tickets: x + 30.
50 + 30 = 80.
So 50 adult tickets and 80 child tickets.
9 Check
Let's check in the story.
80 is 30 more than 50, like the story says.
The money: $1250 plus $1200 makes $2450, 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.