36.4k views
1 vote
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?

User Wyattisimo
by
8.3k points

1 Answer

2 votes
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.
User Ruchin Somal
by
7.9k points