Question 995690: A Mathematics competition contests of 30 multiple-choice questions. 4 marks are awarded for a correct answer while 1 mark is deducted for a wrong answer. No marks will be awarded or decducted for questions not attempted. A student skipped 3 questions and had a score of more than 44. Find the minumum number of correct answers obtained.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you have 30 questions.
he skipped 3 so there are no points awarded or taken away for those.
that leave 27 that are either right or wrong.
you can solve this two ways that i can think of right now.
first way.
set up two equations and solve them simultaneously.
first equation:
4x - y = 44
x is the number of questions he got right and y is the number of questions he got wrong.
second equation:
x + y = 27
the sum of the questions he got right and the sume of the questions he got wrong are equal to 27.
we'll solve using elimination.
4x - y = 44
x + y = 27
add both equations together to get:
5x = 71
divide both sides of the equation by 5 to get:
x = 14.some fraction.
if x is 14, the resulting score will be less than 71.
if x is 15, the resulting score will be greater than 71.
let's do the math to see if this is correct.
when x = 14, the score is 14 * 4 - 13 * 1 = 56 - 13 = 43 which is less than 44.
when x = 15, the score is 15 * 4 - 12 * 1 = 60 - 12 = 48 which is greater than 44.
we used equality to find the break even point and then determined what value x had to be greater than in order to solve the inequality.
second way is this:
we set up the inequality to get:
4x - y > 44
we then set up the equality to get:
x + y = 27
from the equality, we solve for y to get y = 27 - x
we then replace y with 27 - x in the inequality and solve for x.
we get:
4x - y > 44 becomes 4x - (27 - x) > 44
remove parentheses to get 4x - 27 + x > 44
comnbine like terms to get 5x - 27 > 44
add 27 to both sides of the inequality to get 5x > 71.
solve for x to get x > 14.some fraction.
since x has to be an integer, the smallest value that x can be is 15.
same answer derived in different ways.
your solution is that the number of correct solutions has to be greater than 14 and so the minimum number of correct has to be 15.
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