PLEASE HELP
An assistant is in charge of ordering lunch for the monthly office meeting. For the first month, she orders five Falafel wraps, fifteen Turkey BLT sandwiches, and twenty hot Ham and Swiss paninis for a total of $271.25. The next month, she orders eight Falafel wraps, eighteen Turkey BLT sandwiches, and fourteen hot Ham and Swiss paninis for a total of $272. For the third month, she orders twelve Falafel wraps, sixteen Turkey BLT sandwiches, and twelve hot Ham and Swiss paninis for a total of $267. How much does each sandwich cost?

The cost of one Falafel wraps sandwich is $5.75

The cost of one Turkey BLT sandwich is $7.5

The cost of one hot Ham Swiss paninis sandwich is $6.5

Step-by-step explanation:

Here we have for the first month

5 Falafel wraps + 15 Turkey BLT + 20 Ham and Swiss = $271.25

8 Falafel wraps + 18 Turkey BLT + 14 Ham and Swiss = $272

12 Falafel wraps + 16 Turkey BLT + 12 Ham and Swiss = $267

To simplify we have;

5·F + 15·T + 20·H = $271.25(1)

8·F + 18·T + 14·H = $272(2)

12·F + 16·T + 12·H = $267 (3)

Solving the simultaneous equation, we have multiplying equation (1) by 12/5 and subtracting from (3) gives

36·H +20·T  = 384(4)

Multiplying equation (2) by 5/8 and subtracting from (1) gives

45·H + 15·T = 405(5)

Subtract equation (4) from equation (5) multiplied by 20/15  gives

24·H = 156

From which H = 13/2 = $6.5

Plugging the value of H in equation (4) gives

36×13/2 + 20·T = 384

20·T = 150,

∴ T = 150/20 = $7.5

Plugging in the values of H and T in equation (1) we have

5·F + 15·7.5 + 20·6.5= 271.25.

∴ 5·F =  271.25 - ( 15·7.5 + 20·6.5) = 28.75

F = $5.75

Therefore,

The cost of one Falafel wraps sandwich = $5.75

The cost of one Turkey BLT sandwich = $7.5

The cost of one hot Ham Swiss paninis sandwich = $6.5.

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step-by-step explanation: