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Let's break down the problem into parts as stated on the worksheet.

### Part A: 
We are asked to create a linear function to find the total amount of money the school earns by selling $ x $ tickets.

The total cost of the prizes is calculated by adding up the cost of each prize:

- Computer: $349
- Book collection: $42
- Gift certificate: $25
- Pair of movie tickets: $18
- Gift basket: $16

\[
\text{Total cost of prizes} = 349 + 42 + 25 + 18 + 16 = 450
\]

Now, the raffle ticket price is set so that 75 tickets will cover the total cost of the prizes, i.e., the total amount from selling 75 tickets is $450.

The price per ticket is:
\[
\frac{450}{75} = 6 \text{ dollars per ticket}
\]

Thus, the linear function that represents the total amount of money the school earns by selling $ x $ tickets is:
\[
y = 6x
\]
Where:
- $ y $ is the total money earned
- $ x $ is the number of tickets sold

### Part B:
The school’s goal is to raise at least $850 more than the total cost of the prizes. The total goal is:
\[
450 + 850 = 1300 \text{ dollars}
\]

To find the minimum number of raffle tickets, we solve the equation:
\[
6x = 1300
\]
Solving for $ x $:
\[
x = \frac{1300}{6} \approx 216.67
\]

Since you can't sell a fraction of a ticket, the minimum number of tickets to sell is 217.

---

Would you like more details on any step or further clarifications?

### Related Questions:
1. How would the function change if the ticket price were different?
2. What if the school wanted to raise $1000 more than the total cost of the prizes?
3. How many tickets would need to be sold if the total cost of the prizes was $500 instead of $450?
4. Can you express the equation for the profit made, rather than just the total amount of money earned?
5. What would happen if the price per ticket was set at $7 instead of $6?

### Tip:
When creating linear functions in word problems, always identify the base cost or rate and use that to set up the relationship between the variables.

A school is holding a raffle to earn money. This list shows all the prizes in the school’s raffle: 
A computer that costs $349
A book collection that costs $42
A gift certificate that costs $25
A pair of movie tickets that costs $18
A gift basket that costs $16

The raffle ticket price is set so that 75 raffle tickets will pay for all the prizes.

Part A: Create a linear function that can be used to find the total amount of money the school earns by selling x tickets.
Part B: The school’s goal is to raise at least $850 more than the total cost of the prizes. What is the minimum number of raffle tickets that have to be sold in order for the school to reach its goal?

Learn how to solve a linear equation involving a school raffle fundraiser. This problem focuses on calculating total earnings, determining ticket prices, and solving for the number of tickets needed to meet a fundraising goal. Suitable for Grades 9-10.

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