Question

A school is organizing the annual school musical.

These are the costs involved:
Hire of a theater $5000
Hire of costumes $600
Hire of sound equipment for 3 days at $50 per day
Cost to provide the pre-show dinner is $25 per person
Cost of printing is 50 cents per ticket

A survey indicates that 2/5 of the 804 parents of students in the school will attend the musical.

The organisers hope to make a profit of 10%.
How much should they charge for a ticket?
Show full working details, explaining what you are doing at each step and round your answers sensibly.

Answer 1

To determine the ticket price that would allow the organizers to make a 10% profit, we need to calculate the total cost and then add the desired profit margin. Let's break down the costs and work through the calculations step by step.

Hire of theater: $5000

Hire of costumes: $600

Hire of sound equipment for 3 days: $50 per day × 3 days = $150

Cost of providing pre-show dinner: $25 per person Number of parents attending: 2/5 × 804 = 321 parents Cost of providing dinner for parents: $25 × 321 = $8025

Cost of printing: 50 cents per ticket Number of tickets needed: 804 (number of parents) + 804/5 (number of students attending) = 964 Cost of printing tickets: $0.50 × 964 = $482

Total cost: $5000 + $600 + $150 + $8025 + $482 = $14,257

To calculate the ticket price, we need to add the desired profit margin. The profit should be 10% of the total cost.

Profit: 10% × $14,257 = $1425.70

Total amount to be covered (cost + profit): $14,257 + $1425.70 = $15,682.70

Now, we need to divide the total amount by the number of tickets (964) to determine the ticket price.

Ticket price: $15,682.70 / 964 = $16.25 (rounded to the nearest cent)

Therefore, the organizers should charge $16.25 per ticket to achieve a 10%