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

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> 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      Log On


   

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) About Me  (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 x%2By=120

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 x-%281%2F4%29%2Ay=100


x%2By=120 Start with the first equation.


y=120-x Subtract x from both sides.


x-%281%2F4%29%2Ay=100 Move onto the second equation


x-%281%2F4%29%2A%28120-x%29=100 Plug in y=120-x


x-%281%2F4%29%2A%28120%29%2B%281%2F4%29x=100 Distribute


x-120%2F4%2B%281%2F4%29x=100 Multiply


x-30%2B%281%2F4%29x=100 Reduce


4%28x%29-4%2830%29%2Bcross%284%29%28%281%2Fcross%284%29%29x%29=4%28100%29 Multiply EVERY term by the LCD 4 to clear any fractions.


4x-120%2Bx=400 Multiply and simplify


5x-120=400 Combine like terms on the left side.


5x=400%2B120 Add 120 to both sides.


5x=520 Combine like terms on the right side.


x=%28520%29%2F%285%29 Divide both sides by 5 to isolate x.


x=104 Reduce.


So this means that Allan answered 104 questions correctly.