Question

The total number of students and adults at a concert was 460. The cost of tickets was $12 per student and $16 per adult. The total amount of income from tickets was $6520. How many students and how many adults were at the concert?

Answer 1

let the no of students = x
then amount collected from these x students = 12 * x = 12x

Let the number of adults = y
Then amount collected from these y adults = 16 * y = 16y

From the above we get two equations
x + y = 460 ----------(1)
12x + 16y = 6520 ----------(2)

Rearranging (1) we get
x = 460-y ------------------(3)
Substituting this in (2) we get
12(460-y) + 16y = 6520
5520 - 12y + 16y = 6520
4y = 6520 - 5520
y = 1000/4
y = 250
putting this value of y in (3) we get
x= 460 - 250 = 210

so number of students was = x = 210
number of adults was = y = 250