An assistant is in charge of ordering lunch for the monthly office meeting. For the first month, she orders five Falafel, fifteen Turkey BLT sandwiches, and twenty hot Ham and Swiss paninis for a total of $260. The next month, she orders eight Falafel wraps Turkey BLT sandwiches, and 14 hot Ham and Swiss paninis for a total of $263. For the third month, she orders twelve Falafel wraps, 16 Turkey BLT sandwiches, and twelve hot Ham and Swiss paninis fom a total of $258. How much does cach sandwich cost?

The falafel wrap costs $5.50, the turkey BLT costs $7.50, and the ham and swiss panini costs $6.00

Step-by-step explanation:

The first step in solving a system of equations is to write equations to represent each of the situations. We will also define variables to represent each of the sandwiches.

f=cost of falafel wrap

t=cost of Turkey BLT

h=cost of ham and swiss panini

5f+15t+20h=260

8f+18t+14h=263

12f+16t+12h=258

Next, we need to solve the system of equations.

-8/5 (5f+15t+20h=260) multiply equation by - 8/5

-8f-24t-32h=-416 multiply

8f+18t+14h=263 add to another equation to remove a variable

-6t-18h=-153

-12/8 (8f+18t+14h=263) repeat procedure for another equation

-12f-27t-21h=-394.5 multiply

12f+16t+12h=258 combine with another equation

-11t-9h=-136.5

-2 (-11t-9h=-136.5) repeat again by multiplying by - 2

22t+18h=273

-6t-18h=-153 combine the two equations

16t=120

t=7.5

Now we can replace the value of t into the previous equation to find the cost of the ham and swiss panini

22 (7.5) + 18h=273

165+18h=273

18h=108

h=6

Now that we have the cost of two sandwiches, we can find the cost of the falafel wrap by substituting the costs of the sandwiches into the equation.

5f+15 (7.5) + 20 (6) = 260

5f+112.5+120=260

5f+232.5=260

5f=27.5

f=5.5

Therefore the falafel wrap costs $5.50, the turkey BLT costs $7.50, and the ham and swiss panini costs $6.00