Question

On a math test, Johnny made a raw score of 95 on a 40 question test. The correct answers were given 5 points each while incorrect answers deducted 2 points each. If Johnny answered all of the questions, how many questions did Johnny correctly answer?

Answer 1

x - the number of questions he answered correctly
y - the number of questions he answered incorrectly

There were 40 questions on the test.

`x+y=40 \\ y=40-x`

The correct answers were given 5 points each, the incorrect answers were given -2 points each. He made a score of 95.

`5x-2y=95 \\ -2y=95-5x \\ y=-(95)/(2)+(5)/(2)x`

Set 40-x and (-95/2)+(5/2)x equal to each other:

`40-x=-(95)/(2)+(5)/(2)x \\ -x-(5)/(2)x=-(95)/(2)-40 \\ -(2)/(2)x-(5)/(2)x=-(95)/(2)-(80)/(2) \\ -(7)/(2)x=-(175)/(2) \\ x=-(175)/(2) * (-(2)/(7)) \\ x=(175)/(7) \\ x=25`

Johnny answered correctly 25 questions.