An assistant is in charge of ordering lunch for the monthly office meeting. For the first month, she orders ten Falafel wraps, twenty-five Turkey BLT sandwiches, and fifteen hot Ham and Swiss paninis for a total of $361.25. The next month, she orders fifteen Falafel wraps, thirteen Turkey BLT sandwiches, and twenty-two hot Ham and Swiss paninis for a total of $342.50. For the third month, she orders eight Falafel wraps, twenty-two Turkey BLT sandwiches, and twenty hot Ham and Swiss paninis for a total of $359. How much does each sandwich cost?

cost of each Falafel wraps = $6

cost of each Turkey BLT sandwiches: $8

cost of each hot Ham and Swiss paninis: $6.75

Step-by-step explanation:

Let's call:

x: cost of each Falafel wraps

y: cost of each Turkey BLT sandwiches

z: cost of each hot Ham and Swiss paninis

The information can be expressed mathematically as follows:

10x + 25y + 15z = 361.25 (eq. 1)

15x + 13y + 22z = 342.50 (eq. 2)

8x + 22y + 20z = 359 (eq. 3)

subtracting equation 2 to equation 1 multiplied by 1.5, we get:

24.5y + 0.5z = 199.375 (eq. 4)

equation 1 multiplied by 0.8:

8x + 20y + 12z = 289 (eq. 5)

subtracting equation 5 to equation 3:

2y + 8z = 70 (eq. 6)

equation 4 multiplied by 16:

392y + 8z = 3190 (eq. 7)

subtracting equation 6 to equation 7:

390y = 3120

y = 3120/390 = 8

Replacing into equation 6:

2(8) + 8z = 70

z = (70 - 16)/8 = 6.75

Replacing into equation 1:

10x + 25(8) + 15(6.75) = 361.25

x = [361.25 - 25(8) - 15(6.75)]/10 = 6