Chapter 6.4, Problem 26PPE

To determine

To calculate: Number of correct answers and incorrect answers.

Answer to Problem 26PPE

Number of correct answers and incorrect answers are 13 and 7 respectively.

Explanation of Solution

Calculation:

Let’s assumecontestant has given $x$ correct answers and $y$ incorrect answers.

Now, he has given total $20$ answers,

  $\therefore x+y=20$ ….. (i)

The points gained from correct answers are, $150x$

The points lost due to incorrect answers are, $250y$

Now, the final score is,

  $150x-250y=200$ …. (ii)

Now, multiply equation (i) with 250 and add it to (ii),

  $\therefore 150x-250y+250(x+y)=200+5000$

  $\therefore x=13$

Therefore, correct answers given by contestant is $13$

Now, multiply equation (i) with 150 and subtract it from (ii),

  $\therefore 150x-250y-150(x+y)=200-3000$

  $\therefore y=7$

Therefore, incorrect answers given by contestant is $7$