If 77 people attend a concert and tickets for adults cost $2.75 while tickets for children cost $1.5 and total receipts for the concert was $153, how many of each went to the concert?

Question

How many...

Adults?

Children?

Answer 1

If 77 people attend a concert and tickets for adults cost $2.75 while tickets for children cost $1.5 and total receipts for the concert was $153, how many of each went to the concert? How many... Adults? Children?

Detailed Solution:

Let: Number of Adults = x & Number of Children = y, Adults Cost = 2.75x & Children Cost = 1.5y

Total Number of People = Number of Adults + Number of Children = x + y = 77 ==> Equation 1

Total Cost = Adults Cost + Children Cost = 2.75x + 1.5y = 153 ==> Equation 2

Equation 1: x + y = 77 ==> y = 77 − x (Substitute into Equation 2)

Equation 2: 2.75x + 1.5y = 153 ==> 2.75x + 1.5(77 − x) = 153 ==> 2.75x + 115.5 − 1.5x = 153 ==>

1.25x = 153 − 115.5 ==> 1.25x = 37.5 ==> x = 37.5/1.25 ==> x = 30 (Substitute into Equation 1)

y = 77 − x ==> y = 77 − 30 ==> y = 47

Therefore: Number of Adults = x = 30 & Number of Children = y = 47

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 = 30 & y = 47

Answer 2

x = number of adults

y = number of children

2.75x + 1.5y = 153

x + y = 77

Use the substitution method. Subtract x on both sides from the second equation ⇒ y = 77 - x

Then plug in to the first equation to find x.

2.75x + 1.5(77 - x) = 153

2.75x + 115.5 - 1.5x = 153

1.25x + 115.5 = 153

1.25x = 37.5

x = 30

To find y, substitute 30 for x in either of the two original equations.

30 + y = 77 ⇒ y = 47

30 adults and 47 children attended the concert.

Answer 3

x = number of adult tickets

y = number of children's tickets

77 = total number of tickets

2.75x = receipts from adult tickets

1.5x = receipts from child tickets

153 = total receipts

This information can be used to create system of two equations in two unknowns:

x + y = 77

2.75x + 1.5y = 153

using first equation:

y = 77-x

substituting 77-x for y in second equation:

2.75x + 1.5(77-x) = 153

1.25x + 115.5 = 153

x = 30

y = 77-x = 77-30 = 47

Answer 4

A + C = 77

2.75A + 1.5C = 153

1.5A + 1.5C = 77(1.5) =115.5

1.25A=153 -115.5 = 37.5

A =37.5/1.25 = 30 adults

C =77-30 = 47 children

check the solution

2.75(30) + 1.5(47) = 82.5 + 70.5 = 153