Question

A local hamburger shop sold a combined total of 498 hamburgers and cheeseburgers on Tuesday. There were 52 fewer cheeseburgers sold than hamburgers.

Answer 1

C + C+54 = 496

2C+54 = 496

2C = 442

C = 221 (number of cheeseburgers sold)

Answer 2

275 hamburgers and 223 cheeseburgers were sold on Tuesday.

Solution:

Assume hamburgers as H and cheeseburgers as C,

From the given,

Total number of hamburgers and cheeseburgers sold on Tuesday is 498 i.e.
`H+C=498 \rightarrow H=498-C \rightarrow (1)`

There were 52 fewer cheeseburgers sold than hamburgers i.e.
`H-C=52 \rightarrow (2)`

On substituting (1) in (2) we get,

`498-C-C=52 \rightarrow 498-2C=52 \rightarrow 498-52=2C`

`\Rightarrow 446=2C \rightarrow (446)/(2)=C \rightarrow C=223 \rightarrow (3)`

On substituting (3) in(1) we get,

`H=498-223=275`

`\therefore H=275 \text{ and } C=223`