Question

A local hamburger shop sold a combined total of 578 hamburgers and cheeseburgers on Tuesday. There were 72 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Tuesday?

Answer 1

Hey there! :)

h = hamburgers sold

2h - 72 = 578

2h = 650
 2       2

h = 325

There were 72 fewer cheeseburgers sold than hamburgers. That means cheeseburgers = 325 - 72

325 - 72 =  253

253 = cheeseburgers
325 = hamburgers

253 + 325 = 578

Hamburgers = 325

Hope this helps :)

Answer 2

Let h be hamburgers and c be cheeseburgers.
We know that $h + c = 578$
We also know that $c + 72 = h$
This gives us a system of equations we can solve. My preferred method to solve systems is substitution, where we solve one equation for one of the variables, then substitute that solution in the other equation, reducing it to a single variable equation. One of the equations already equals h, so we can go straight into the sub part.
$h + c = 578$
$(c + 72) + c = 578$
$c2 = 506$
$c = 253$
Finally, we go back to the other equation and solve for h.
$c + 72 = h$
$253 + 72 = h$
$325 = h$
So, total there were 253 cheeseburgers sold, and 325 hamburgers sold.