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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?

Respuesta :

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:

They sold 513 turkey sandwiches.

Step-by-step 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 = [tex]t+s=925[/tex]

Total income = [tex]4t+6s=4524[/tex]

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

  • Isolate t for [tex]t+s=925[/tex] => [tex]t=925-s[/tex]
  • Substitute [tex]t=925-s[/tex] into [tex]4t+6s=4524[/tex]

[tex]4\left(925-s\right)+6s=4524[/tex]

  • Solve for s

[tex]3700-4s+6s=4524\\3700+2s=4524\\3700+2s-3700=4524-3700\\2s=824\\\frac{2s}{2}=\frac{824}{2}\\s=412[/tex]

  • For [tex]t=925-s[/tex] substitute s = 412

[tex]t=925-412\\t=513[/tex]

They sold 513 turkey sandwiches and 412 steak sandwiches.

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