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Bunuel
ABC Company projects that it will sell 48,000 units of product X per year at a unit price of $1, 12,000 units per year at $2 per unit, and 3,000 units per year at $4 per unit. Which of the following equations could define the projected number of units sold per year (N), as a function of price per unit (P)?

(A) \(N = \frac{48,000}{p^2 +2}\)

(B) \(N = \frac{48,000}{p^2}\)

(C) \(N = \frac{48,000}{p + 14}\)

(D) \(N = \frac{48,000}{p + 4}\)

(E) \(N = \frac{48,000}{p^2 +8}\)



We try to find p as a function of N = 48000 / N

When N = 48000, we get p = 48000 / 48000 = 1

When N = 12000, we get p = 48000 / 12000 = 4. Since p = $2, then this is \(p^2\)

When N = 3000, we get p = 48000 / 3000 = 16. Since p = $4, then this is \(p^2\)


Option B

Arun Kumar


Why is the numerator taken as 48000 in all the equations ?
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Bunuel
ABC Company projects that it will sell 48,000 units of product X per year at a unit price of $1, 12,000 units per year at $2 per unit, and 3,000 units per year at $4 per unit. Which of the following equations could define the projected number of units sold per year (N), as a function of price per unit (P)?

(A) \(N = \frac{48,000}{p^2 +2}\)

(B) \(N = \frac{48,000}{p^2}\)

(C) \(N = \frac{48,000}{p + 14}\)

(D) \(N = \frac{48,000}{p + 4}\)

(E) \(N = \frac{48,000}{p^2 +8}\)
Solution:

We see that for choice B, when p = 1, then N = 48,00/1^2 = 48,000, and it’s the only choice that yields 48,000 when p = 1. Furthermore, when p = 2, then N = 48,000/2^2 = 12,000, and when p = 4, then N = 48,000/4^2 = 3,000. Therefore, B is the correct answer.

Answer: B
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