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 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