The Broadstreet Bulletin, a small local newspaper, will begin selling monthly subscriptions to access its web-based content. Market research indicates that the newspaper can use the expression –12p+600 to determine the number of subscriptions it will sell in its first month depending on the subscription price, p. The newspaper wants to make enough money from subscriptions in its first month to cover its operating costs of $7,200.What two subscription prices will make the newspaper exactly $7,200 in revenue in its first month?
Question
The Broadstreet Bulletin, a small local newspaper, will begin selling monthly subscriptions to access its web-based content. Market research indicates that the newspaper can use the expression –12p+600 to determine the number of subscriptions it will sell in its first month depending on the subscription price, p. The newspaper wants to make enough money from subscriptions in its first month to cover its operating costs of 7,200 in revenue in its first month?
Solution
To solve this problem, we first need to understand that the revenue made by the newspaper is the product of the price per subscription and the number of subscriptions sold. This can be represented by the equation:
Revenue = price * number of subscriptions
The number of subscriptions sold is given by the expression -12p + 600, and the revenue is given as $7200. So we can set up the equation as:
7200 = p(-12p + 600)
Solving this equation will give us the two possible prices for the subscriptions.
First, distribute the p across the expression in the parentheses:
7200 = -12p^2 + 600p
Rearrange the equation to set it equal to zero:
0 = 12p^2 - 600p + 7200
This is a quadratic equation, and we can solve it using the quadratic formula:
p = [-(-600) ± sqrt((-600)^2 - 4127200)] / (2*12)
Solving this gives us:
p = [600 ± sqrt(360000 - 345600)] / 24
p = [600 ± sqrt(14400)] / 24
p = [600 ± 120] / 24
So the two possible prices for the subscriptions are p = 720/24 = 20.
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