MHB How Many Questions Did Jenny Answer Correctly to Achieve a Raw Score of 12?

[Jameson]

On a certain test, the raw score is calculated as follows: 1 point is awarded for each correct answer and 1/4 of a point is deducted for each incorrect answer. If Jenny answered all of the questions, [math]q[/math], on the test and earned a raw score of 12, how many questions did she answer correctly?

Note: A question must be marked correct or incorrect, there is no partial credit.

Remember to read the http://www.mathhelpboards.com/threads/773-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!

 

[Jameson]

Congratulations to the following members for their correct solutions:

1) Sudharaka
2) Reckoner
3) veronica1999

Solution:
[sp]We start with three variables in a sense: the number of correct questions, the number of incorrect questions and the number of total questions. These can be reduced to two variable by noting that [math]c+i=q[/math] thus [math]i=q-c[/math]

So if she gets 1 point for every question correct, c, and -1/4 point for every incorrect question, i or (q-c) then her raw score can be found by:

[math]c-\frac{1}{4}(q-c)=12[/math]

Solving for c we get: [math]c=\frac{q+48}{5}[/math] [/sp]