Question

A cafe only sells two types of sandwiches, turkey, and steak. The cafe charges $4 for turkey sandwiches and $6 for steak sandwiches. Last month, the cafe sold $4524 worth of sandwiches. The cafe sold a total of 925 sandwiches.

How many turkey sandwiches did they sell?

Answer 1

t + s = 925....s = 925 - t
4t + 6s = 4524

4t + 6(925 - t) = 4524
4t + 5550 - 6t = 4524
-2t = 4524 - 5550
-2t = -1026
t = 1026/2
t = 513 <== 513 turkey sandwiches

t + s = 925
513 + s = 925
s = 925 - 513
s = 412 <=== 412 steak sandwiches

Answer 2

They sold 513 turkey sandwiches.

Explanation:

Let t be the number of turkey sandwiches and s be the number of steak sandwiches.

With these variables, we can create equations for the totals they've given us:

Total sandwiches =
`t+s=925`

Total income =
`4t+6s=4524`

Now we can solve the system for the number of turkey sandwiches and steak sandwiches

• Isolate t for
  `t+s=925` =>
  `t=925-s`

• Substitute
  `t=925-s` into
  `4t+6s=4524`

`4\left(925-s\right)+6s=4524`

• Solve for s

`3700-4s+6s=4524\\3700+2s=4524\\3700+2s-3700=4524-3700\\2s=824\\(2s)/(2)=(824)/(2)\\s=412`

• For
  `t=925-s` substitute s = 412

`t=925-412\\t=513`

They sold 513 turkey sandwiches and 412 steak sandwiches.