https://file.aiquickdraw.com/mathbot/file/172729652211908y9v6nb.jpg

The problem provided involves finding the correct equation to represent the relationship between the number of adult tickets (denoted by $ x $) and the total amount of money raised from the sale of the tickets.

Here is a breakdown of the problem:

- A company sold a total of 150 tickets.
- The cost of an adult ticket is \$10.
- The cost of a child ticket is \$6.
- The number of adult tickets sold is $ x $, and therefore the number of child tickets sold is $ 150 - x $ (since the total number of tickets is 150).

The total amount raised from the sale of tickets is the sum of the money from adult and child tickets:
- Amount from adult tickets: $ 10x $.
- Amount from child tickets: $ 6(150 - x) $.

Thus, the total amount $ y $ is given by:

\[
y = 10x + 6(150 - x)
\]

Simplifying the equation:

\[
y = 10x + 900 - 6x
\]
\[
y = 4x + 900
\]

Now let's match this with the given choices in the image:

- **A**: $ 6x + 10y = 150 $ - Incorrect structure.
- **B**: $ 10x + 6y = 150 $ - Incorrect structure.
- **C**: $ y = 6x + 10(150 - x) $ - This is a valid option if expanded and simplified.
- **D**: $ y = 10x + 6(150 - x) $ - This is the correct option and matches our derived equation.

So, the correct answer is **D**.

Would you like further clarification or details on this solution?

Here are some related questions to expand your understanding:

1. How can you set up similar equations for more complex scenarios with different prices for tickets?
2. What happens if the total number of tickets sold is different, say 200 tickets?
3. How can we represent the number of child tickets as a function of adult tickets and total tickets?
4. What is the role of simplifying equations in solving word problems like this one?
5. How would the equation change if the price of child tickets was higher than adult tickets?

**Tip:** Always identify the variables in word problems and write expressions for each type of contribution before setting up the equation!

A company sold a total of 150 adult and child tickets to a fundraiser. The company charged $10 for each adult ticket and $6 for each child ticket. Which equation represents the relationship between the number of adult tickets sold (x) and the total amount, y, in dollars, raised from the sale of the tickets?

Find the equation representing the relationship between adult ticket sales (x) and the total amount raised (y) when adult tickets are priced at $10 and child tickets at $6. This problem uses linear equations to determine the correct relationship. Suitable for Grades 8-10.

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