How many of each

Question

240 students go to prom.

A total of $2,100 is spent on food.

How many students order chicken at a cost of $12 and how many order pasta which costs $8?

Answer 1

This is a system of equations with two variables problem.

Let x = number of students who order chicken

Let y = number of students who order pasta

EQ 1. x + y = 240

EQ 2. 12x + 8y = 2100

We can rewrite Equation 1 as y = 240 -x

We can then substitute that in for y in EQ2

12x + 8(240-x) = 2100

12x + 1920 -8x = 2100

4x +1920 = 2100

4x =180

x= 45

Since y=240-x...y= 240-45...so y = 195

45 ordered chicken and 195 ordered pasta