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Answer:
<em>There were 8 correct answers and 2 incorrect answers.</em>
Step-by-step explanation:
The contest consists of paying $50 for each correctly answered question and subtracting $25 for each incorrectly answered question.
Let's call:
x = Number of correct answers
y = Number of incorrect answers
The resident from a dormitory answered 10 questions last week. This leads to the following condition:
Since each correct answer adds $50 and each incorrect answer subtracts $25, the weekly balance is
50x - 25y
The contestant earned $350, thus:
50x - 25y = 350
Dividing by 25:
2x - y = 14
Adding this equation with [1]:
x + 2x = 24
Simplifying:
3x = 24
x = 24 / 3
x = 8
From [1]:
y = 10 - x = 10 - 8
y = 2
There were 8 correct answers and 2 incorrect answers.