Step by step
The question
Question: Shirts cost $10 and hats cost $6.
Max can spend at most $60.
Can he buy 3 hats and 4 shirts?
1 Find what we know
What do we know?
Shirts cost $10 each.
Hats cost $6 each.
Max can spend $60 or less.
What do we want?
To know if 3 hats and 4 shirts fit.
2 Name the unknowns
We don't know how many shirts.
We call that number x.
We don't know how many hats either.
It is a different number, so it gets its own letter: y.
3 Write the inequality
One shirt costs $10.
So x shirts cost 10 times x: 10x.
One hat costs $6.
So y hats cost 6 times y: 6y.
At most $60 means $60 or less.
That is the sign less than or equal to.
In words: the shirt money plus the hat money is at most $60.
So the inequality is 10x + 6y ≤ 60.
Careful!
At most means 60 or less.
So the sign is less than or equal to, not more than.
4 Put the point in
4 shirts: x = 4.
3 hats: y = 3.
As a point, that is (4, 3).
We put them in.
Is it less than or equal to 60?
We don't know yet.
10 times 4 is 40.
6 times 3 is 18.
40 plus 18 is 58.
Is 58 less than or equal to 60?
Yes.
True!
5 Answer the question
Yes: 4 shirts and 3 hats cost $58.
6 Check
Let's check with the money.
$2 is left, not below 0.
So Max can pay.
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.