A local hamburger shop sold a combined total of 396 hamburgers and cheeseburgers on Sunday. There were 54 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Sunday?

Answer 1

There are two unknowns: the number of hamburgers and the number of cheeseburgers.

Let h = number of hamburgers and c = number of cheeseburgers

Then based off the first part of the problems, since we have a total of 396 burgers

h + c = 396

From the second piece of information, c = h - 54.

To solve, substitute h - 54 for c in the first equation.

So, h + (h - 54) = 396

2h - 54 = 396

2h = 450

h = 225

c is 54 less than h so c = 171.

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Answer 2

Using x for hamburger quantity and y for cheeseburger quantity, we can solve with the equations

x + y = 396

x - y = 54

With substitution, we can see that

x = 396 - y

(396 - y) - y = 54

y = 171,

which means that x = 396 - 171 = 225