20 p = 20 q - 20 r - 20 s The given equation relates the positive variables p ,

Question

20 p = 20 q - 20 r - 20 s The given equation relates the positive variables p , q , r , and s . Which of the following is equivalent to q ?

Accepted Answer

Choice C is correct. Multiplying each side of the given equation by 1 20 yields 1 20 20 p = 1 20 20 q - 20 r - 20 s . Distributing 1 20 on each side of this equation yields 20 20 p = 20 20 q - 20 20 r - 20 20 s , or 1 p = 1 q - 1 r - 1 s . Adding 1 r + 1 s to each side of this equation yields 1 s + 1 r + 1 p = 1 q . Multiplying 1 s by p r p r , 1 r by p s p s , and 1 p by r s r s yields p r p r s + p s p r s + r s p r s = 1 q , which is equivalent to p r + p s + r s p r s = 1 q . Since p r + p s + r s p r s = 1 q , and it's given that p , q , r , and s are positive, it follows that the reciprocals of each side of this equation are also equal. Thus, p r s p r + p s + r s = q 1 , or p r s p r + p s + r s = q . Therefore, p r s p r + p s + r s is equivalent to q . Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.

Question 20-p-2