If 112 people attend a concert and tickets for adults cost $3.75 while tickets for children cost $1.75 and total receipts for the concert was $330, how many of each went to the concert?

Question

___ adults

___ children

Answer 1

If 112 people attend a concert and tickets for adults cost $3.75 while tickets for children cost $1.75 and total receipts for the concert was $330, how many of each went to the concert? ___ adults ___ children

Detailed Solution:

Let: Number of Adults = x & Number of Children = y, Adults Cost = 3.75x & Children Cost = 1.75y

Total Number of People = Number of Adults + Number of Children = x + y = 112 ==> Equation 1

Total Cost = Adults Cost + Children Cost = 3.75x + 1.75y = 330 ==> Equation 2

Equation 1: x + y = 112 ==> y = 112 − x (Substitute into Equation 2)

Equation 2: 3.75x + 1.75y = 330 ==> 3.75x + 1.75(112 − x) = 330 ==> 3.75x + 196 − 1.75x = 330 ==>

2x = 330 − 196 ==> 2x = 134 ==> x = 134/2 ==> x = 67 (Substitute into Equation 1)

y = 112 − x ==> y = 112 − 67 ==> y = 45

Therefore: Number of Adults = x = 67 & Number of Children = y = 45

Note: You can solve this easily using TI-84 Plus Matrix:

Create 2 x 3 Matrix A ==> (Enter the value of x, y, ...) ==> Go to: Matrix Math ==> Chose: rref(A) =

rref(A) = x = 67 & y = 45

Answer 2

Let x = the number of adult tickets

Let y = the number of child tickets

x+y = 112

3.75x+1.75y = 330

Can you solve this by substitution or elimination?