Question

1. a theater is selling tickets to a play. adult tickets cost $8 each and children’s tickets cost $5 each. they collect $275 after selling x adult tickets and y children’s tickets. what does the point (30,7) mean in the context of this situation? is the point (5,15) a solution to the given problem? explain your reasoning.

Explanation:

Step1: Understand the variables

In the context of the problem, \(x\) represents the number of adult tickets sold and \(y\) represents the number of children's tickets sold.

Step2: Analyze the point \((30,7)\)

For the point \((30,7)\), since \(x = 30\) and \(y=7\), it means 30 adult tickets and 7 children's tickets were sold.

Step3: Check if \((5,15)\) is a solution

The total money collected is given by the equation \(8x + 5y\). Substitute \(x = 5\) and \(y = 15\) into the equation:

$$
LATEXBLOCK0
$$

Since \(115
eq275\), the point \((5,15)\) is not a solution.

Answer:

• The point \((30,7)\) means 30 adult tickets and 7 children's tickets were sold.
• The point \((5,15)\) is not a solution because when \(x = 5\) and \(y = 15\), \(8x + 5y=8\times5+5\times15 = 115

eq275\).