SOLUTION: A mathematics contest consists of 26 questions. Seven points are awarded for each correct answer, and 3 points are deducted for each wrong answer. If a question is omitted, no poi

Question 298196: A mathematics contest consists of 26 questions. Seven points are awarded for each
correct answer, and 3 points are deducted for each wrong answer. If a question is omitted, no points are awarded. If Daniel gets a score of 76 on the contest, how many questions did he answer correctly?

Answer by amoati(11) (Show Source): You can put this solution on YOUR website!
if X is the number of correct answers, Y the number of wrong answers, Z is the number of omitted questions then:

X + Y + Z = 26 --> (1)
And
7 X - 3 Y = 76 --> (2)
Multiplying (1) by 3 then 3 X + 3 Y + 3 Z = 78 then summing it to (2) then
10 X + 3 Z = 154
since X and Z are integers then Z Must be 8 and X would be 13, the next possible solution for the above equation is 18 & 10 which is invalid (greater than the total number of questions)
So the number of correct answers is 13, number of wrong answers is 5 and the number of omitted questions is 8

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