I have the following problem solving question:
In a multiple choice test of 25 questions, four marks are given for each correct answer and two marks are deducted for each wrong answer. One mark is deducted for any question which is not attempted. James scores 55 marks and wants to know how many questions he got right. He can't remember how many questions he did not attempt, but he doesn't think it was very many. How many questions did James get right?
I've worked out that he gained $2.2$ marks per question on average and lost $1.8$ marks per question on average (because $55/25$ is $2.2$ and $4-2.2$ is $1.8$).
I've also stated that $2x+y=45$, where $x$ is the number of questions he got wrong and $y$ is the number of questions he didn't answer. Consequently, $100-(2x+y)=55$.
Additionally, I know that getting every question wrong would result in $-50$ total marks, not answering any question would result in $-25$, and answering all correctly would result in $100$.
However, I don't know what to do with any of this information.
Best Answer
Let the number of correct answers be $C$, number of wrong answers be $W$, and number of unattempted answers be $N$.
$$C+W+N=25$$ $$4C-2W-N=55$$
Eliminating $C$, $$6W+5N=45$$
Therefore, $$W=0, N=9$$ or $$W=5, N=3$$
If you consider $9$ as many, then
$$C=17, W=5, N=3$$