Step by step
The question
Question: Cakes cost $7 and pies cost $11.
Ali spends $73.
Write the equation.
1 Find what we know
What do we know?
Cakes cost $7 each.
Pies cost $11 each.
Ali spends $73 in all.
What do we want?
An equation for this story.
2 Name the unknowns
We don't know how many cakes.
We call that number x.
We don't know how many pies either.
It is a different number, so it gets its own letter: y.
3 Write the equation
One cake costs $7.
So x cakes cost 7 times x: 7x.
One pie costs $11.
So y pies cost 11 times y: 11y.
In words: the cake money plus the pie money makes all the money.
So the equation is 7x + 11y = 73.
Careful!
x + y counts the cakes and pies, not the money.
The money is 7x + 11y.
4 Check
Let's test the equation with one buy that costs $73.
We try 1 cake first.
1 cake costs $7.
$66 is left.
66 divided by 11 is 6: 6 pies.
Put x = 1 and y = 6 in: 7 plus 66 is 73.
The equation works!
Let's look back.
First: find what we know.
Then: name the unknowns.
Then: write the equation.
Last: check.