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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineToday's cafeteria specials at a high school in Oakdale are a deluxe turkey sandwich and a chef salad. During early lunch, the cafeteria sold 3535 turkey sandwiches and 3333 chef salads, for a total of $134\$134. During the late lunch, 6565 turkey sandwiches and 7070 chef salads were sold, for a total of $275\$275. How much does each item cost?\newlineA turkey sandwich costs $_\$\_, and a chef salad costs $_\$\_.

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineToday's cafeteria specials at a high school in Oakdale are a deluxe turkey sandwich and a chef salad. During early lunch, the cafeteria sold 3535 turkey sandwiches and 3333 chef salads, for a total of $134\$134. During the late lunch, 6565 turkey sandwiches and 7070 chef salads were sold, for a total of $275\$275. How much does each item cost?\newlineA turkey sandwich costs $_\$\_, and a chef salad costs $_\$\_.
  1. Define variables, set equations: Step 11: Define the variables and set up the equations based on the given information.\newlineLet xx be the cost of a turkey sandwich and yy be the cost of a chef salad.\newlineFrom early lunch sales: 35x+33y=13435x + 33y = 134\newlineFrom late lunch sales: 65x+70y=27565x + 70y = 275
  2. Use elimination method: Step 22: Use elimination to solve the system of equations. Choose to eliminate xx by making the coefficients of xx equal.\newlineMultiply the first equation by 6565 and the second equation by 3535:\newline(65)(35x+33y)=65(134)(65)(35x + 33y) = 65(134)\newline(35)(65x+70y)=35(275)(35)(65x + 70y) = 35(275)
  3. Simplify equations: Step 33: Simplify the equations from Step 22.\newline2275x+2145y=87102275x + 2145y = 8710\newline2275x+2450y=96252275x + 2450y = 9625
  4. Eliminate x, solve for y: Step 44: Subtract the first new equation from the second to eliminate x.\newline2275x+2450y−(2275x+2145y)=9625−87102275x + 2450y - (2275x + 2145y) = 9625 - 8710\newline305y=915305y = 915
  5. Solve for y: Step 55: Solve for y.\newliney = 915305\frac{915}{305}\newliney = 33
  6. Substitute yy to solve xx: Step 66: Substitute y=3y = 3 back into the first original equation to solve for xx.35x+33(3)=13435x + 33(3) = 13435x+99=13435x + 99 = 13435x=3535x = 35x=1x = 1

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