A school is holding a carnival and hopes to raise $\$ 500$. Child tickets cost $\$ 3$ and adult tickets cost $\$ 5$. If the school sells $x$ child tickets and $y$ adult tickets, then the equation $3 x+5 y=500$ expresses the fact that the school raised exactly $\$ 500$ from ticket sales. 1. Solve the equation for $x$. 2. Explain when it might be helpful to rewrite the equation this way.

Step 1 ：The question asks to solve the equation \(3x + 5y = 500\) for \(x\). This means we need to isolate \(x\) on one side of the equation. To do this, we can subtract \(5y\) from both sides of the equation.

Step 2 ：The solution is \(x = \frac{500}{3} - \frac{5y}{3}\). This means that for any given number of adult tickets sold (\(y\)), we can calculate the number of child tickets (\(x\)) that need to be sold in order to raise exactly $500.

Step 3 ：Final Answer: \(x = \boxed{\frac{500}{3} - \frac{5y}{3}}\)

Step 4 ：Rewriting the equation in this way might be helpful in situations where we know the number of adult tickets sold and want to find out how many child tickets need to be sold to reach a certain fundraising goal. It can also be useful in creating a graph or a table to visualize the relationship between the number of adult and child tickets sold.