A contestant on a quiz show gets 50 points for every correct answer and loses 100 points for each incorrect answer. After answering 24 questions, the contestant has 300 points. How many questions has the contestant answered correctly? Incorrectly?
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To solve this problem, let's assume the contestant has answered "x" questions correctly and "y" questions incorrectly.
According to the given information, for every correct answer, the contestant gains 50 points, so the total points gained from correct answers is 50x.
For every incorrect answer, the contestant loses 100 points, so the total points lost from incorrect answers is 100y.
Since the contestant has answered 24 questions in total, the sum of correct and incorrect answers can be written as:
x + y = 24
From the given information, we know that the contestant has a total of 300 points, so we can set up another equation:
50x - 100y = 300
Now we have a system of two equations with two unknowns:
x + y = 24
50x - 100y = 300
To solve this system, we can use the method of substitution or elimination. Let's use the method of substitution here.
Rearrange the first equation to solve for x in terms of y:
x = 24 - y
Substitute this value of x in the second equation:
50(24 - y) - 100y = 300
1200 - 50y - 100y = 300
-150y = -900
y = 6
Now substitute the value of y back into the first equation to find x:
x + 6 = 24
x = 24 - 6
x = 18
Therefore, the contestant has answered 18 questions correctly and 6 questions incorrectly.