Question

1. a theater is selling tickets to a play. adult tickets cost $8 each and childrens tickets cost $5 each. they collect $275 after selling x adult tickets and y childrens tickets.

Explanation:

Step1: Set up the equation

The total money collected is the sum of money from adult tickets and children's tickets. The money from adult tickets is \(8x\) (since each adult ticket costs \(\$8\)) and the money from children's tickets is \(5y\) (since each children's ticket costs \(\$5\)). So the equation is \(8x + 5y=275\).

Step2: Use the point \((30,7)\) to check the equation

Substitute \(x = 30\) and \(y = 7\) into the left - hand side of the equation: \(8\times30+5\times7\).
First, calculate \(8\times30 = 240\) and \(5\times7=35\).
Then \(8\times30 + 5\times7=240 + 35=275\).

Answer:

The point \((30,7)\) satisfies the equation \(8x + 5y = 275\), which means when \(30\) adult tickets and \(7\) children's tickets are sold, the total money collected is \(\$275\).