Step by step
The question
Question: Shirts cost $12 and hats cost $8.
Ana spends $96.
Write the equation.
1 Find what we know
What do we know?
Shirts cost $12 each.
Hats cost $8 each.
Ana spends $96 in all.
What do we want?
An equation for this story.
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 equation
One shirt costs $12.
So x shirts cost 12 times x: 12x.
One hat costs $8.
So y hats cost 8 times y: 8y.
In words: the shirt money plus the hat money makes all the money.
So the equation is 12x + 8y = 96.
Careful!
x + y counts the shirts and hats, not the money.
The money is 12x + 8y.
4 Check
Let's test the equation with one buy that costs $96.
We try 1 shirt first.
1 shirt costs $12.
$84 is left.
84 divided by 8 is not a whole number.
We can't buy part of a hat.
Next try.
2 shirts cost $24.
$72 is left.
72 divided by 8 is 9: 9 hats.
Put x = 2 and y = 9 in: 24 plus 72 is 96.
The equation works!
Let's look back.
First: find what we know.
Then: name the unknowns.
Then: write the equation.
Last: check.