Finding number of ticket purchases both under and over eighteen years of age.

Question

31,000 individuals are predicted to attend your festival. Tixkets for under eighteens are $106 each and over eighteens are $115 eacj. The total revenue from ticket sales is $3,452,923. Find the total number of attendees that are under eighteen and over eighteen. Show all working out.

Answer 1

The first step is to assign variables to what we are trying to solve for:

x = under 18 attendees

y = over 18 attendees

The next step is to form equation from what is given:

1. x + y = 31,000
2. 106 * x + 115 * y = 3,452,923

Solve for one variable and then substitute it into the other equation:

x + y = 31,000

x = 31,000 - y

106 * (31,000 - y) + 115 * y = 3,452,923

3,286,000 - (106 * y) + 115 * y = 3,452, 923

-106 * y + 115 * y = 166,923

9 * y = 166,923

y = 18, 547

x = 31,000 - y

x = 31,000 - 18,547

x = 12,453

There are 12,453 attendees under 18 and 18,547 attendees over 18 at the festival.

Answer 2

31,000 individuals are predicted to attend your festival. Tickets for under eighteens are $106 each and over eighteens are $115 each. The total revenue from ticket sales is $3,452,923. Find the total number of attendees that are under eighteen and over eighteen. Show all working out.

THIS ANSWER HAS BEEN CORRECTED ON 8/23/19

Let the attendees under 18 be = C for children.

Let the attendees over 18 be = A for adults.

C + A = 31,000

$106*C + $115*A = $3,452,923

Rearrange C + A = 31,000 to C = 31,000 - A

Substitute this in the other equation:

$106*(31,000 - A) + $115*(A) = $3,452,923

$3286000 - $106A + $115A = $3,452,923

$9 A = $3,452,923 - $3,286,000

A = $166,923 / $9

A = 18,547

So C + A = 31,000 becomes C + 18,547 = 31,000

C = 31,000 - 18,547 = 12453

12,453 attendees were under 18 and 18,547 attendees were over 18 is the answer that you seek.

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Thanks!

John B.

Atlanta, GA