Problem
Test 2 Score: $0 / 20 \quad 0 / 20$ answered Question 20 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 $\$ 260$. The next month, she orders eight Falafel wraps, eighteen 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 for a total of \$258. How much does each sandwich cost? Falafel Wrap $=\$$ Turkey BLT $=\$$ Hot Ham and Swiss $=\$$ Submit Question
Solution
Step 1 ：Let's denote the price of Falafel wrap as F, the price of Turkey BLT as T, and the price of Hot Ham and Swiss as H.
Step 2 ：From the problem, we can set up the following system of linear equations: \(5F + 15T + 20H = 260\), \(8F + 18T + 14H = 263\), and \(12F + 16T + 12H = 258\).
Step 3 ：Solving this system of equations, we find that F = \(\frac{11}{2}\), H = 6, and T = \(\frac{15}{2}\).
Step 4 ：Thus, the price of each sandwich is: Falafel Wrap = \(\boxed{\$5.50}\), Turkey BLT = \(\boxed{\$7.50}\), and Hot Ham and Swiss = \(\boxed{\$6.00}\).
