Step by step
The question
Question: Apples cost $2 and pears cost $3.
Mia spends $20.
Write the equation.
1 Find what we know
What do we know?
Apples cost $2 each.
Pears cost $3 each.
Mia spends $20 in all.
What do we want?
An equation for this story.
2 Name the unknowns
We don't know how many apples.
We call that number x.
We don't know how many pears either.
It is a different number, so it gets its own letter: y.
3 Write the equation
One apple costs $2.
So x apples cost 2 times x: 2x.
One pear costs $3.
So y pears cost 3 times y: 3y.
In words: the apple money plus the pear money makes all the money.
So the equation is 2x + 3y = 20.
Careful!
x + y counts the apples and pears, not the money.
The money is 2x + 3y.
4 Check
Let's test the equation with one buy that costs $20.
We try 1 apple first.
1 apple costs $2.
$18 is left.
18 divided by 3 is 6: 6 pears.
Put x = 1 and y = 6 in: 2 plus 18 is 20.
The equation works!
Let's look back.
First: find what we know.
Then: name the unknowns.
Then: write the equation.
Last: check.