Step by step
The question
Question: Balls cost $5 and bats cost $15.
Kim spends $65.
Can she buy 4 balls and 3 bats?
1 Find what we know
What do we know?
Balls cost $5 each.
Bats cost $15 each.
Kim spends $65 in all.
What do we want?
To know if 4 balls and 3 bats fit.
2 Name the unknowns
We don't know how many balls.
We call that number x.
We don't know how many bats either.
It is a different number, so it gets its own letter: y.
3 Write the equation
One ball costs $5.
So x balls cost 5 times x: 5x.
One bat costs $15.
So y bats cost 15 times y: 15y.
In words: the ball money plus the bat money makes all the money.
So the equation is 5x + 15y = 65.
Careful!
x + y counts the balls and bats, not the money.
The money is 5x + 15y.
4 Put the point in
4 balls: x = 4.
3 bats: y = 3.
As a point, that is (4, 3).
We put them in.
Is it equal to 65?
We don't know yet.
5 times 4 is 20.
15 times 3 is 45.
20 plus 45 is 65.
Is 65 equal to 65?
Yes.
True!
5 Answer the question
Yes: 4 balls and 3 bats cost $65.
6 Check
Let's check with the money.
Nothing is left over and nothing is missing.
So it is exactly right.
It works!
Let's look back.
First: find what we know.
Then: name the unknowns.
Then: write the equation.
Then: put the point in.
Then: answer the question.
Last: check.