Step by step
The question
Question: Shirts cost $12 and hats cost $8.
Ana can spend at most $100.
Can she buy 5 shirts and 4 hats?
1 Find what we know
What do we know?
Shirts cost $12 each.
Hats cost $8 each.
Ana can spend $100 or less.
What do we want?
To know if 5 shirts and 4 hats 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 $12.
So x shirts cost 12 times x: 12x.
One hat costs $8.
So y hats cost 8 times y: 8y.
At most $100 means $100 or less.
That is the sign less than or equal to.
In words: the shirt money plus the hat money is at most $100.
So the inequality is 12x + 8y ≤ 100.
Careful!
At most means 100 or less.
So the sign is less than or equal to, not more than.
4 Put the point in
5 shirts: x = 5.
4 hats: y = 4.
As a point, that is (5, 4).
We put them in.
Is it less than or equal to 100?
We don't know yet.
12 times 5 is 60.
8 times 4 is 32.
60 plus 32 is 92.
Is 92 less than or equal to 100?
Yes.
True!
5 Answer the question
Yes: 5 shirts and 4 hats cost $92.
6 Check
Let's check with the money.
$8 is left, not below 0.
So Ana 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.