SOLUTION: Hi In a maths quiz containing 10 questions 4 points are awarded for each correct answer 1 point is deducted for each wrong answer and no points for each blank answer. How many sc

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Question 1208821: Hi
In a maths quiz containing 10 questions 4 points are awarded for each correct answer 1 point is deducted for each wrong answer and no points for each blank answer. How many scores are possible.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52903) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let k be the number of correct answers,  0 <= k <= 10.


Then the number of wrong answers is 10-k.


The formula for the score as the function of "k" is

    S(k) = 4k - (10-k) = 5k - 10.


So, when k =   0,  1, 2, 3,  4,  5,  6,  7,  8,  9, 10,  the values for S(k) are

             -10, -5, 0, 5, 10, 15, 20, 25, 30, 35, 40 .


Thus, 11 different values of scores are possible.

Solved.



Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


The response from the other tutor goes much deeper into the problem than necessary.

The possible number of right answers is 0 to 10, which is 11 possibilities; the scores for all of those possibilities are different. Since the problem only asks for how many scores are possible, the answer is 11.

ANSWER: 11