A student responded to all of the 22 questions on a test and received a score of 63.5. If the scores were derived by adding 3.5 points for each correct answer and deducting 1 point for each incorrect answer, how many questions did the student answer incorrectly?
Let the number of correct answers be X
The number of incorrect answers will be 22-X
For each correct answer the student got 3.5 points for a total of 3.5X
For each incorrect answer one point was taken out which is equivalent to -(22-X)
The total he got for that was 63.5
So in short you have the following equation and solution.
3.5X-(22-X) = 63.5
3.5X-22+X = 63.5
4.5X = 63.5+22
4.5X = 85.5
4.5X/4.5 = 85.5/4.5
X = 19
So incorrect answers will be 22-X = 22-19 = 3.