A quiz has thirty questions whose answers can only be correct or incorrect.
A correct answer scores 8 points, but 3 points are deducted for every incorrect answer.
Harry did the quiz and scored a total of 152 points. How many questions did he get correct?
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Suppose Harry got x correct answers and y incorrect answers.
For the x correct answers, he scored 8 x points
For the y incorrect answers, 3 y points were deducted.
So, Harry's score = ( 8 x − 3 y ) points.
But we are told Harry scored a total of 1 5 2 points.
8 x − 3 y = 1 5 2 . . . . . . . . . . ( 1 )
We also know there were 3 0 questions altogether
x + y = 3 0 . . . . . . . . . . ( 2 )
Multiply ( 2 ) by 3 :
8 x − 3 y = 1 5 2 . . . . . . . . . ( 1 )
3 x + 3 y = 9 0 . . . . . . . . . ( 3 )
Add equations ( 1 ) and ( 2 ) :
1 1 x = 2 4 2
x = 2 2