Step by step
The question
Question: Cups cost $4 and plates cost $6.
Ben can spend at most $50.
Can he buy 5 cups and 6 plates?
1 Find what we know
What do we know?
Cups cost $4 each.
Plates cost $6 each.
Ben can spend $50 or less.
What do we want?
To know if 5 cups and 6 plates fit.
2 Name the unknowns
We don't know how many cups.
We call that number x.
We don't know how many plates either.
It is a different number, so it gets its own letter: y.
3 Write the inequality
One cup costs $4.
So x cups cost 4 times x: 4x.
One plate costs $6.
So y plates cost 6 times y: 6y.
At most $50 means $50 or less.
That is the sign less than or equal to.
In words: the cup money plus the plate money is at most $50.
So the inequality is 4x + 6y ≤ 50.
Careful!
At most means 50 or less.
So the sign is less than or equal to, not more than.
4 Put the point in
5 cups: x = 5.
6 plates: y = 6.
As a point, that is (5, 6).
We put them in.
Is it less than or equal to 50?
We don't know yet.
4 times 5 is 20.
6 times 6 is 36.
20 plus 36 is 56.
Is 56 less than or equal to 50?
No.
That is false.
5 Answer the question
No: 5 cups and 6 plates cost $56.
6 Check
Let's check with the money.
Ben would need $6 more.
So Ben can't.
It works!
Let's look back.
First: find what we know.
Then: name the unknowns.
Then: write the inequality.
Then: put the point in.
Then: answer the question.
Last: check.