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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 Cedarburg are a deluxe turkey sandwich and a chef salad. During early lunch, the cafeteria sold 4444 turkey sandwiches and 6767 chef salads, for a total of $400\$400. During the late lunch, 2828 turkey sandwiches and 4040 chef salads were sold, for a total of $244\$244. 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 Cedarburg are a deluxe turkey sandwich and a chef salad. During early lunch, the cafeteria sold 4444 turkey sandwiches and 6767 chef salads, for a total of $400\$400. During the late lunch, 2828 turkey sandwiches and 4040 chef salads were sold, for a total of $244\$244. How much does each item cost?\newlineA turkey sandwich costs $\$_____, and a chef salad costs $\$_____.
  1. Set up equations: Step 11: Set up the system of equations based on the given data.\newlineLet xx be the cost of a turkey sandwich and yy be the cost of a chef salad.\newlineFrom early lunch sales: 44x+67y=40044x + 67y = 400\newlineFrom late lunch sales: 28x+40y=24428x + 40y = 244
  2. Use elimination method: Step 22: Use elimination to solve the system of equations.\newlineMultiply the first equation by 2828 and the second by 4444 to align the coefficients for xx:\newline(44x+67y)×28=400×28(44x + 67y) \times 28 = 400 \times 28\newline(28x+40y)×44=244×44(28x + 40y) \times 44 = 244 \times 44\newline1232x+1876y=112001232x + 1876y = 11200\newline1232x+1760y=107361232x + 1760y = 10736
  3. Solve for y: Step 33: Subtract the second equation from the first to eliminate xx:1876y−1760y=11200−107361876y - 1760y = 11200 - 10736116y=464116y = 464y=464116y = \frac{464}{116}y=4y = 4
  4. Substitute to find x: Step 44: Substitute y=4y = 4 back into one of the original equations to find xx:44x+67(4)=40044x + 67(4) = 40044x+268=40044x + 268 = 40044x=400−26844x = 400 - 26844x=13244x = 132x=13244x = \frac{132}{44}x=3x = 3

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