Question

What is the answer for this question? Why would it be helpful to rewrite the equation that way?

Answer 1

To solve the equation for "x", we will use operations in both sides of the equation.

$3x+5y=500$

First, we already have the "x" in the left side, but there is also a term with "y", so let's put it to the right side.

to do this, we can substract "5y" in both sides:

$\begin{gathered} 3x+5y-5y=500-5y \\ 3x=500-5y \end{gathered}$

Now, we just need to pass the "3" to the other side, which we can do by dividing both sides by 3:

$\begin{gathered} \frac{3x}{3}=\frac{500-5y}{3} \\ x=\frac{500}{3}-\frac{5}{3}y \end{gathered}$

Tha is the equation solved for "x".

This way of writing the equation can be usefull if we want to calculate "x" for a given "y" value, that is, if we know the number of adult tickets sold, we can substitute it into the equation in this form and just evaluate the right part to obtain the "x" value.