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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 :

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

There were 40 questions on the test.
[tex]x+y=40 \\ y=40-x[/tex]

The correct answers were given 5 points each, the incorrect answers were given -2 points each. He made a score of 95.
[tex]5x-2y=95 \\ -2y=95-5x \\ y=-\frac{95}{2}+\frac{5}{2}x [/tex]

Set 40-x and (-95/2)+(5/2)x equal to each other:
[tex]40-x=-\frac{95}{2}+\frac{5}{2}x \\ -x-\frac{5}{2}x=-\frac{95}{2}-40 \\ -\frac{2}{2}x-\frac{5}{2}x=-\frac{95}{2}-\frac{80}{2} \\ -\frac{7}{2}x=-\frac{175}{2} \\ x=-\frac{175}{2} \times (-\frac{2}{7}) \\ x=\frac{175}{7} \\ x=25[/tex]

Johnny answered correctly 25 questions.

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