Question

A deli has two platters of sandwiches. The first platter costs $33

and you get 2 turkey sandwiches and 3 roast beef sandwiches.
The other platter costs $32 and you get 3 turkey sandwiches and
2 roast beef sandwiches. Let x represent the cost of each
turkey sandwich and y represent the cost of each
roast beef sandwich. What is the system of linear equations
for the given scenario? What is the cost of each sandwich?

Answer 1

Let x be the cost of each turkey sandwich and y be the cost of each roast beef sandwich.

From the first platter, which costs $33 and contains 2 turkey sandwiches and 3 roast beef sandwiches, we can write the equation:

2x + 3y = 33

From the second platter, which costs $32 and contains 3 turkey sandwiches and 2 roast beef sandwiches, we can write the equation:

3x + 2y = 32

Now we have a system of two linear equations in two variables:

2x + 3y = 33

3x + 2y = 32

To solve for x and y, we can use the method of elimination. Multiplying the first equation by 2 and the second equation by -3, we get:

4x + 6y = 66

-9x - 6y = -96

Adding these equations, we get:

-5x = -30

Dividing both sides by -5, we get:

x = 6

Now we can substitute x = 6 into either of the original equations to solve for y. Using the first equation, we get:

2(6) + 3y = 33

12 + 3y = 33

3y = 21

y = 7

Therefore, each turkey sandwich costs $6 and each roast beef sandwich costs $7.