Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. Today's cafeteria specials at a high school in Middletown are a deluxe turkey sandwich and a chef salad. During early lunch, the cafeteria sold 21 turkey sandwiches and 17 chef salads, for a total of 110 During the late lunch 12 turkey sandwiches and 56 chef salads were sold, for a total of 248 How much does each item cost? A turkey sandwich costs and a chef salad costs

To solve this problem, we need to set up a system of equations based on the information given. Let's define the variables first:- Let be the cost of a turkey sandwich.- Let be the cost of a chef salad.We can then write the following system of equations based on the sales during early and late lunch:1. For early lunch: 2. For late lunch: Now we will solve this system using the elimination method.First, we need to make the coefficients of one of the variables the same in both equations. We'll eliminate by finding a common multiple for the coefficients of in both equations. The least common multiple of 21 and 12 is 84.We will multiply the first equation by 4 and the second equation by 7 to make the coefficients of equal: Now we subtract the first modified equation from the second modified equation to eliminate : Now that we have the value of , we can substitute it back into one of the original equations to solve for . We'll use the first equation: So, the cost of a turkey sandwich is .A turkey sandwich costs .