SAT Math Problem (26)

Question

R = ^F /_{N + F} 

 

A website uses the formula above to calculate a seller's rating, R, based on the number of favorable reviews, F, and unfavorable reviews, N. Which of the following expresses the number of favorable reviews in terms of other variables?

 

A. F = (RN)/(R-1)

B. F = (RN)/(1-R)

C. F = (N)/(1-R)

D. F = (N)/(R-1)

Answer 1

Pari,

 

We need to get all F's on one side and everything else on the other:

 

R = F/(N + F)

 

Multiply each side by (N + F):

 

R(N + F) = F

 

RN + RF = F

 

RN = F - RF

 

RN = (1 - R)F (factoring F out of both terms)

 

Divide both sides by (1 - R)

 

RN/(1 - R) = F

 

B is correct

Answer 2

R = F/(N + F)

 

R(N + F) = F

 

RN + RF = F

 

RN = F - RF = F(1 - R)

 

F = RN/(1 - R)