A primary school is planning to hold a fete, but needs help in figuring out how much to charge for entry. they intend to have an 'all you can eat' sausages sizzle, and they think each adult will eat about $3 worth of sausages and each child $2 worth. The cost of cleaning after the event will be $300. They want an adult ticket to cost twice as much as a child ticket, and they expect that, on average , 1.7 parents and 2.3 children will come from each family. How much will they need to charge for adult and child tickets if they are expecting 120 families to attend and they don't want to make a porfit or a loss?

Cost of sausages for parents = $3 x 120 x 1.7 = $612

Cost of sausages for children = $2 x 120 x 2.3 = $552

Total Cost (including cleaning) = $612 + $552 + $300 = $1464

Assume ticket cost for parents to be 'a' and children to be 'b'.

Then, a = 2b

Now, since the ticket price needs to be exactly equal to the cost,

120 (1.7a + 2.3b) = 1464 ;
or, 120 {1.7(2b) + 2.3b) = 1464 ;
or, 3.4b + 2.3b = 12.2;
or, 5.7b = 12.2;
or, b = 2.14

Then, a = 2b = 2 x 2.14 = 4.28

Therefore, tickets will cost $2.14 for children and $4.28 for adults.

To calculate how much the primary school should charge for adult and child tickets in order to break even, we need to consider the cost of sausages and cleaning after the event. Here's how we can calculate it step-by-step:

1. Calculate the total cost of sausages:
- Assuming each adult will eat $3 worth of sausages, the total cost for all adults can be calculated as:
Total cost for adults = Number of adults * Cost per adult sausage
- Similarly, for children who will eat $2 worth of sausages, the total cost for all children can be calculated as:
Total cost for children = Number of children * Cost per child sausage

2. Calculate the total cost of cleaning:
- The cost of cleaning after the event is given as $300.

3. Calculate the total cost of the event:
Total cost = Total cost of sausages + Total cost of cleaning

4. Calculate the number of adults and children attending:
- If on average 1.7 parents and 2.3 children are expected from each family, the total number of adults can be calculated as:
Number of adults = Number of families * Average adults per family
- Similarly, the total number of children can be calculated as:
Number of children = Number of families * Average children per family

5. Calculate the revenue needed:
- As the adult ticket is supposed to cost twice as much as the child ticket, we can represent the child ticket price as 'x' and the adult ticket price as '2x'.
- The total revenue needed can be calculated as:
Revenue needed = (Number of adults * Price per adult ticket) + (Number of children * Price per child ticket)

6. Equate the total cost and the revenue needed:
Total cost = Revenue needed

7. Solve for the child ticket price (x) and adult ticket price (2x) using the equation built in step 6.

Let's plug in the given values to calculate the ticket prices step-by-step:
- Number of families = 120
- Average adults per family = 1.7
- Average children per family = 2.3
- Cost per adult sausage = $3
- Cost per child sausage = $2
- Cost of cleaning = $300

Step 1:
- Total cost for adults = Number of adults * Cost per adult sausage
= (Number of families * Average adults per family) * Cost per adult sausage
= (120 * 1.7) * 3
= 612

- Total cost for children = Number of children * Cost per child sausage
= (Number of families * Average children per family) * Cost per child sausage
= (120 * 2.3) * 2
= 552

Step 2:
- Total cost of cleaning = $300

Step 3:
- Total cost = Total cost of sausages + Total cost of cleaning
= 612 + 552 + 300
= 1,464

Step 4:
- Number of adults = Number of families * Average adults per family
= 120 * 1.7
= 204

- Number of children = Number of families * Average children per family
= 120 * 2.3
= 276

Step 5:
- Revenue needed = (Number of adults * Price per adult ticket) + (Number of children * Price per child ticket)
= (204 * 2x) + (276 * x)

Step 6:
- Total cost = Revenue needed
= 1,464

- Substituting the revenue needed from step 5:
1,464 = (204 * 2x) + (276 * x)

Step 7:
- Solve this equation to find the values of x and 2x.

To calculate the ticket prices for adults and children, we need to consider the costs and expected number of attendees. Let's break down the problem step by step:

1. Calculate the total cost of sausages:
- Each adult is expected to eat $3 worth of sausages.
- Each child is expected to eat $2 worth of sausages.
- The number of adults can be calculated as: 1.7 parents * 120 families = 204 adults.
- The number of children can be calculated as: 2.3 children * 120 families = 276 children.
- Total cost of sausages = (Cost per adult * Number of adults) + (Cost per child * Number of children)

2. Calculate the total revenue needed to cover costs:
- The cost of cleaning after the event is $300.
- Total revenue needed = Total cost of sausages + Cost of cleaning

3. Determine the ratio of adult ticket price to child ticket price:
- The adult ticket price is twice the child ticket price.

4. Calculate the ticket prices for adults and children:
- Let x be the child ticket price.
- The adult ticket price would be 2x.

5. Find the ticket prices that ensure no profit or loss:
- Total revenue from ticket sales = (Adult ticket price * Number of adults) + (Child ticket price * Number of children)
- Set the total revenue from ticket sales equal to the total revenue needed to cover costs, and solve for x.

Let's calculate the ticket prices:

Step 1:
Number of adults = 1.7 * 120 = 204
Number of children = 2.3 * 120 = 276
Cost per adult = $3
Cost per child = $2
Total cost of sausages = (3 * 204) + (2 * 276)

Step 2:
Cost of cleaning = $300
Total revenue needed = Total cost of sausages + Cost of cleaning

Step 3:
Ratio of adult ticket price to child ticket price = 2:1

Step 4:
Let x be the child ticket price.
Adult ticket price = 2x

Step 5:
Total revenue from ticket sales = (Adult ticket price * Number of adults) + (Child ticket price * Number of children)
Set this equal to the total revenue needed to cover costs:
(2x * 204) + (x * 276) = Total revenue needed

Solve this equation to find the value of x, which will give us the child ticket price. Then, multiply the child ticket price by 2 to get the adult ticket price.