Quiz!

Algebra Level 2

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?

Try this: All of my problems


The answer is 22.

Munem Shahriar by Munem Shahriar , 18, Bangladesh

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1 solution

Munem Shahriar
Aug 8, 2017

Suppose Harry got x x correct answers and y y incorrect answers.

For the x x correct answers, he scored 8 x 8x points

For the y y incorrect answers, 3 y 3y points were deducted.

So, Harry's score = ( 8 x − 3 y ) = (8x - 3y) points.

But we are told Harry scored a total of 152 152 points.

8 x − 3 y = 152.......... ( 1 ) 8x -3y = 152 .......... (1)

We also know there were 30 30 questions altogether

x + y = 30.......... ( 2 ) x + y = 30.......... (2)

Multiply ( 2 ) (2) by 3 : 3:

8 x − 3 y = 152......... ( 1 ) 8x - 3y = 152 ......... (1)

3 x + 3 y = 90......... ( 3 ) 3x + 3y = 90 ......... (3)

Add equations ( 1 ) (1) and ( 2 ) : (2):

11 x = 242 11x = 242

x = 22 x = \color{#3D99F6} \boxed{22}

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