The Vilas County News earns a profit of $20 per year for each of its 3,000 subscribers. Management projects that the profit per subscriber would increase by 1¢ for each additional subscriber over the current 3,000. How many subscribers are needed to bring a total profit of $153,525?
850
To determine the number of subscribers needed to bring a total profit of $153,525, we can use the given information to set up an equation.
Let's start by determining the total profit from the existing 3,000 subscribers. We know that the Vilas County News earns a profit of $20 per year for each subscriber, so the profit from the current subscribers will be:
Profit from 3,000 subscribers = $20 * 3,000 = $60,000
The management projects that the profit per subscriber would increase by 1¢ for each additional subscriber. This means that for every additional subscriber, the profit will increase by an extra $0.01.
Let's assume that the number of additional subscribers needed is "x". Since the profit per subscriber increases by 1¢, the additional profit will be:
Additional profit = $0.01 * x
Therefore, the total profit with the additional subscribers will be:
Total profit = $60,000 + Additional profit = $60,000 + ($0.01 * x)
Now we can set up an equation to solve for "x":
$60,000 + ($0.01 * x) = $153,525
To solve for "x", let's subtract $60,000 from both sides of the equation:
$0.01 * x = $153,525 - $60,000
$0.01 * x = $93,525
Now, divide both sides of the equation by $0.01 to isolate "x":
x = $93,525 / $0.01
x = 9,352,500
Therefore, you would need approximately 9,352,500 additional subscribers to bring a total profit of $153,525.
Keep in mind that this number might be an approximation, as it assumes a linear relationship between the number of subscribers and the profit per subscriber. Also, it's essential to consider other factors, such as market saturation and feasibility, before aiming for such a significant increase in subscribers.