Final answer:
John would make $10,350 after 9 years.
Step-by-step explanation:
In this problem, John's popcorn sales vary directly with the time he spends selling. This means that the amount he makes is directly proportional to the time he spends. We can write a direct variation equation as y = kx, where y is the amount made in dollars and x is the time spent in years. To solve the problem, we need to find the value of constant k.
Given that John made $2300 in popcorn sales over 2 years, we can substitute these values into the equation: 2300 = k * 2. Solving for k, we divide both sides by 2 to get k = 1150.
Now that we know the value of k, we can use it to find the amount John would make after 9 years. We substitute 9 for x in the equation: y = 1150 * 9 = 10350. Therefore, John would make $10,350 after 9 years.