Question 105552
The students are only scored on the questions they answer.
(a) The best score would be 50 questioned all answered correctly
{{{3*50 = 150}}} answer
(b) The worst score would be 50 qestions all answered incorrectly
{{{-1*50 = -50}}}
(c) The raw score would be {{{3*C - (A - C)}}}, where
A = the number of questions answered, and
C = the number of questions answered correctly
I want the worst score of -50 to correspond to 0
I want the best score of 150 to correspond to 100
For the worst score to equal 0, I need to add 50, so I have
{{{3C - (A - C) + 50}}}
{{{3*0 - (50 - 0) + 50 = 0}}} this is true
Now I have to make the best score = 100
{{{k(3*50 - (50 - 50)) + 50 = 100}}}
{{{k(150 - 50 + 50) + 50 = 100}}}
solve for k
{{{150k = 50}}}
{{{k = 1/3}}}
So the score is {{{1/3*(3C - (A - C)) + 50}}}
(d)C = 38
   I = 4
   A = 50 - 8 = 42
{{{1/3*(3C - (A - C)) + 50}}}
{{{1/3*(3*38 - (42 - 38)) + 50}}}
{{{1/3*(114 - 4) + 50}}}
{{{1/3*110 + 50 = 86.66}}} answer