Step by step
The question
Question: Adult tickets cost $9 and child tickets cost $6.
Sam spends $60.
Write the equation.
1 Find what we know
What do we know?
Adult tickets cost $9 each.
Child tickets cost $6 each.
Sam spends $60 in all.
What do we want?
An equation for this story.
2 Name the unknowns
We don't know how many adult tickets.
We call that number x.
We don't know how many child tickets either.
It is a different number, so it gets its own letter: y.
3 Write the equation
One adult ticket costs $9.
So x adult tickets cost 9 times x: 9x.
One child ticket costs $6.
So y child tickets cost 6 times y: 6y.
In words: the adult ticket money plus the child ticket money makes all the money.
So the equation is 9x + 6y = 60.
Careful!
x + y counts the adult tickets and child tickets, not the money.
The money is 9x + 6y.
4 Check
Let's test the equation with one buy that costs $60.
We try 1 adult ticket first.
1 adult ticket costs $9.
$51 is left.
51 divided by 6 is not a whole number.
We can't buy part of a child ticket.
Next try.
2 adult tickets cost $18.
$42 is left.
42 divided by 6 is 7: 7 child tickets.
Put x = 2 and y = 7 in: 18 plus 42 is 60.
The equation works!
Let's look back.
First: find what we know.
Then: name the unknowns.
Then: write the equation.
Last: check.