Question

1. tickets to greendale high school soccer game cost $7 for adults and $5 for students. there is a total of 150 tickets sold for $850. how many adult tickets are sold and how many student tickets are sold?

let statements:
equations:
solution (as an ordered pair)
does it make sense?
interpret:

Explanation:

Step 1: Define Variables

Let \( x \) be the number of adult tickets and \( y \) be the number of student tickets.

Step 2: Set Up Equations

We have two equations:

1. From the total number of tickets: \( x + y = 150 \)
2. From the total cost: \( 7x + 5y = 850 \)

Step 3: Solve the System of Equations

From the first equation, we can express \( y \) in terms of \( x \): \( y = 150 - x \)
Substitute \( y = 150 - x \) into the second equation:
\[

$$\begin{align*} 7x + 5(150 - x) &= 850 \\ 7x + 750 - 5x &= 850 \\ 2x + 750 &= 850 \\ 2x &= 850 - 750 \\ 2x &= 100 \\ x &= 50 \end{align*}$$

\]
Then find \( y \) using \( y = 150 - x \): \( y = 150 - 50 = 100 \)

Step 4: Check if the Solution Makes Sense

• Total number of tickets: \( 50 + 100 = 150 \), which matches the given total.
• Total cost: \( 7\times50 + 5\times100 = 350 + 500 = 850 \), which also matches the given total. So the solution makes sense.

Step 5: Interpret the Solution

The ordered pair \( (50, 100) \) means that 50 adult tickets and 100 student tickets were sold.

Answer:

The number of adult tickets sold is 50 and the number of student tickets sold is 100. The solution \( (50, 100) \) makes sense as it satisfies both the total number of tickets and the total cost conditions.