The caterers for the Immaculata prom dinner and dance are preparing two different meals: chicken for $12/meal or pasta for $8/meal. The total cost of the dinners for 240 students is $2100. Create and solve a linear system to determine the number of chicken dishes and the number of pasta dishes that need to be served.

Answer 1

Let x be the number of chicken dishes and y be the number of pasta dishes.

The total number of meals is given by:
x + y = 240

The total cost of meals is given by:
12x + 8y = 2100

Multiplying the first equation by -8, we have -8x - 8y = -1920.

Adding this equation to the second equation, we get:
12x + 8y + (-8x - 8y) = 2100 + (-1920)
4x = 180
x = 45

Substituting this value into the first equation, we find:
45 + y = 240
y = 195

Therefore, the number of chicken dishes that need to be served is 45 and the number of pasta dishes that need to be served is 195.