Final answer:
By solving a system of linear equations, we determine the cost of one turkey sandwich is $5 and one avocado sandwich is $3. Hence, the cost of 1 turkey sandwich and 2 avocado sandwiches is $11, which corresponds to answer choice B.
Step-by-step explanation:
The question involves solving a system of linear equations to determine the cost of one turkey sandwich and two avocado sandwiches. We have two equations based on the given scenarios:
- 5T + 5A = $40 (five turkey sandwiches and five avocado sandwiches)
- 6T + 3A = $39 (six turkey sandwiches and three avocado sandwiches)
Let's denote the cost of a turkey sandwich as T and the cost of an avocado sandwich as A. We can solve these equations simultaneously to find the values of T and A.
First, we can multiply the first equation by 3 and the second equation by 5, and then subtract the second equation from the first to eliminate A:
- (3)(5T + 5A) = 3($40)
- (5)(6T + 3A) = 5($39)
After simplification, we get basic equations:
- 15T + 15A = $120
- 30T + 15A = $195
Subtracting the equations, we get:
15T = $75 => T = $5
Now we can substitute T = $5 into one of the original equations to find the value of A:
5T + 5A = $40
5($5) + 5A = $40
$25 + 5A = $40
5A = $15 => A = $3
Therefore, the cost of one turkey sandwich (T) is $5 and the cost of one avocado sandwich (A) is $3. To find the cost of 1 turkey sandwich and 2 avocado sandwiches:
1T + 2A = 1($5) + 2($3) = $5 + $6 = $11
The cost of 1 turkey sandwich and 2 avocado sandwiches is $11.