Step by step
The question
Question: Pens cost $2 and notebooks cost $5.
Leo spends $29.
Write the equation.
1 Find what we know
What do we know?
Pens cost $2 each.
Notebooks cost $5 each.
Leo spends $29 in all.
What do we want?
An equation for this story.
2 Name the unknowns
We don't know how many pens.
We call that number x.
We don't know how many notebooks either.
It is a different number, so it gets its own letter: y.
3 Write the equation
One pen costs $2.
So x pens cost 2 times x: 2x.
One notebook costs $5.
So y notebooks cost 5 times y: 5y.
In words: the pen money plus the notebook money makes all the money.
So the equation is 2x + 5y = 29.
Careful!
x + y counts the pens and notebooks, not the money.
The money is 2x + 5y.
4 Check
Let's test the equation with one buy that costs $29.
We try 1 pen first.
1 pen costs $2.
$27 is left.
27 divided by 5 is not a whole number.
We can't buy part of a notebook.
Next try.
2 pens cost $4.
$25 is left.
25 divided by 5 is 5: 5 notebooks.
Put x = 2 and y = 5 in: 4 plus 25 is 29.
The equation works!
Let's look back.
First: find what we know.
Then: name the unknowns.
Then: write the equation.
Last: check.