Question

At a recent charity event there was a range of admission charges:

Family (2 Adults + 2 Children)

Adult

Senior

Child (5 to 16 years)

Child under-5

$44

$14

$12

$10

Free

In addition it was possible to buy Family tickets before the event at the reduced cost of $40 per

family.

At the gate tickets to the value of $40 000 were purchased, and prepaid tickets added a further

$10000 to the total income. For every Family ticket sold on the day, 1 Adult, 1 Senior, and 3 Child

tickets were sold and 2 under-5 children were admitted free of charge.

How many people attended?

A

B

c

4400

4600

4650

5400

Answer 1

5400

Explanation:

Given data

Family (2 Adults + 2 Children) = $44

Adult = $14

Senior = $12

Child (5 to 16 years) = $10

Child under-5 = Free

At reduced price family buys ticket at = $40

Total prepaid ticket sold = $10,000

Value of ticket sold at the gate = $40,000

Determine how many people attended

first step : determine number of family that purchased the prepaid tickets

= 10,000 / 40 = 250 families

∴ number people who booked prepaid tickets = 250 * 4 = 1000 people

Next step : Determine the number of families that booked the ticket at the gate

let the number of families = y

40,000 = 44 y + 12y + 3y * 10 + 14y + 2y *0

40,000 = y ( 100 ) hence y = 40,000 / 100 = 400

∴ number of people = 400 * ( 4 + 1 + 1 + 3 + 2 ) = 400 * 11 = 4400

Number of people whom attended = 4400 + 1000 = 5,400