Step by step
The question
Question: Lamps cost $35 and rugs cost $50.
Dan spends $255.
Write the equation.
1 Find what we know
What do we know?
Lamps cost $35 each.
Rugs cost $50 each.
Dan spends $255 in all.
What do we want?
An equation for this story.
2 Name the unknowns
We don't know how many lamps.
We call that number x.
We don't know how many rugs either.
It is a different number, so it gets its own letter: y.
3 Write the equation
One lamp costs $35.
So x lamps cost 35 times x: 35x.
One rug costs $50.
So y rugs cost 50 times y: 50y.
In words: the lamp money plus the rug money makes all the money.
So the equation is 35x + 50y = 255.
Careful!
x + y counts the lamps and rugs, not the money.
The money is 35x + 50y.
4 Check
Let's test the equation with one buy that costs $255.
We try 1 lamp first.
1 lamp costs $35.
$220 is left.
220 divided by 50 is not a whole number.
We can't buy part of a rug.
Next try.
2 lamps cost $70.
$185 is left.
185 divided by 50 is not a whole number.
We can't buy part of a rug.
Next try.
3 lamps cost $105.
$150 is left.
150 divided by 50 is 3: 3 rugs.
Put x = 3 and y = 3 in: 105 plus 150 is 255.
The equation works!
Let's look back.
First: find what we know.
Then: name the unknowns.
Then: write the equation.
Last: check.