A newspaper's profit is $21 per year for each of its 4,500 subscribers. Management estimates that the profit per subscriber will increase by 1¢ or 0.01 for each additional subscriber over the current 4,500. How many subscribers will bring a total profit of $130,000?
I got 1689.67, but the answer must be rounded and to a whole number I got 1690. But that answer isn't correct.
I got 1689.67, but the answer must be rounded and to a whole number I got 1690. But that answer isn't correct.
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Let x = # of additional subscribers.
130000 = (4500 + x)(21 + 0.01x)
130000 = 94500 + 45x + 21x + 0.01x^2
0 = 0.01x^2 + 66x - 35500
0 = 0.01(x^2 + 6600x - 3550000)
0 = x^2 + 6600x - 3550000
0 = (x + 7100)(x - 500)
x = -7100 or x = 500
A negative number of subscribers makes no sense (-7100 + 4500 = -2600), so discard x = -7100,
leaving just x = 500
# of subscribers = 4500 + 500 = 5000
130000 = (4500 + x)(21 + 0.01x)
130000 = 94500 + 45x + 21x + 0.01x^2
0 = 0.01x^2 + 66x - 35500
0 = 0.01(x^2 + 6600x - 3550000)
0 = x^2 + 6600x - 3550000
0 = (x + 7100)(x - 500)
x = -7100 or x = 500
A negative number of subscribers makes no sense (-7100 + 4500 = -2600), so discard x = -7100,
leaving just x = 500
# of subscribers = 4500 + 500 = 5000