Step by step
The question
Question: Large pizzas cost $15 and small pizzas cost $10.
Raj spends $85.
Write the equation.
1 Find what we know
What do we know?
Large pizzas cost $15 each.
Small pizzas cost $10 each.
Raj spends $85 in all.
What do we want?
An equation for this story.
2 Name the unknowns
We don't know how many large pizzas.
We call that number x.
We don't know how many small pizzas either.
It is a different number, so it gets its own letter: y.
3 Write the equation
One large pizza costs $15.
So x large pizzas cost 15 times x: 15x.
One small pizza costs $10.
So y small pizzas cost 10 times y: 10y.
In words: the large pizza money plus the small pizza money makes all the money.
So the equation is 15x + 10y = 85.
Careful!
x + y counts the large pizzas and small pizzas, not the money.
The money is 15x + 10y.
4 Check
Let's test the equation with one buy that costs $85.
We try 1 large pizza first.
1 large pizza costs $15.
$70 is left.
70 divided by 10 is 7: 7 small pizzas.
Put x = 1 and y = 7 in: 15 plus 70 is 85.
The equation works!
Let's look back.
First: find what we know.
Then: name the unknowns.
Then: write the equation.
Last: check.