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Advanced Math Difficulty: Medium

$P = N (19 - C)$

The given equation relates the positive numbers $P$ , $N$ , and $C$ . Which equation correctly expresses $C$ in terms of $P$ and $N$ ?

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Explanation

Choice D is correct. It's given that the values of $P$ , $N$ , and $C$ are positive. Therefore, dividing each side of the given equation by $N$ yields $\frac{P}{N} = 19 - C$ . Subtracting $19$ from each side of this equation yields $\frac{P}{N} - 19 = - C$ . Dividing each side of this equation by $negative 1$ yields $19 - \frac{P}{N} = C$ , or $C = 19 - \frac{P}{N}$ .

Choice A is incorrect. This equation is equivalent to $P = N C - 19$ , not $P = N (19 - C)$ .

Choice B is incorrect. This equation is equivalent to $P = 19 - N C$ , not $P = N (19 - C)$ .

Choice C is incorrect. This equation is equivalent to $P = N (C - 19)$ , not $P = N (19 - C)$ .