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?

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Question: 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?

Solution:
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.

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