`S = (C - 1/4 I)/(C+I)`
A techer uses the formula above to calculate her students' scores, S, by subtracting `1/4` of the number of equations the students answered incorrectly, I, from the number of questions they answered correctly, C, and dividing by the total number of questions. Which of the following expresses the number of questions answered incorrectly in terms of the other variables ?

Options

A. `(C(1-4S))/(4S+1)`
B. `(C(1+4S))/(4S-1)`
C. `(4C(1-S))/(4S+1)`
D. `(4C(1+S))/(4S-1)`

Answer

C

Explanation

Clear the equation of the fraction in the numerator by multiplying both sides by 4 to yield:
`4S=(4C-l)/(C+l)`
Now, multiply botyh sides by the denominator `C + l` to clear the equation of fractions :
`4S(C+l) = 4C-l`
Distribute the 4S:
`4SC+4Sl=4C-l`
To solve for l, collect all the terms that include l on one side of the equation:
`4Sl +l=4C-4SC`
Factor out the l:
`l (4S+1) =4C-4SC`
Divide to isolate l, and facto out 4c from the numerator:
`l =(4c -4SC)/(4S+1) =(4C(1-S))/(4S+1)`
(C ) is correct.