SOLUTION: Hi, I am having a problem with the following question. On a test containing 120 questions, the final score is based on 1 point for each correct answer and 1/4 of a point subtrac

Question 195674: Hi, I am having a problem with the following question.
On a test containing 120 questions, the final score is based on 1 point for each correct answer and 1/4 of a point subtracted for each incorrect answer. Allan answered all of the questions and received a final score of 100 points. How many questions did Allan answer correctly?
Thank you for your help!
Melissa
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let
x = number of correct answers
y = number of incorrect answers

Since there are 120 questions and you can only get a correct or incorrect answer, this means that

Also, since "the final score is based on 1 point for each correct answer and 1/4 of a point subtracted for each incorrect answer" and Allan "received a final score of 100 points", this means that

Start with the first equation.

Subtract x from both sides.

Move onto the second equation

Plug in

Distribute

Multiply

Reduce

Multiply EVERY term by the LCD to clear any fractions.

Multiply and simplify

Combine like terms on the left side.

Add to both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

So this means that Allan answered 104 questions correctly.
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