# Problem of the week #12 - June 18th, 2012

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#### Jameson

Staff member
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, $$\displaystyle q$$, 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.

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• Reckoner and Sudharaka

#### Jameson

Staff member
Congratulations to the following members for their correct solutions:

1) Sudharaka
2) Reckoner
3) veronica1999

Solution:
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 $$\displaystyle c+i=q$$ thus $$\displaystyle i=q-c$$

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:

$$\displaystyle c-\frac{1}{4}(q-c)=12$$

Solving for c we get: $$\displaystyle c=\frac{q+48}{5}$$

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