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noname [10]
3 years ago
6

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 incorrec

t answers deducted 2 points each. If Johnny answered all of the questions, how many questions did Johnny correctly answer?
Mathematics
1 answer:
Sidana [21]3 years ago
8 0
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=-\frac{95}{2}+\frac{5}{2}x


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

Johnny answered correctly 25 questions.
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