Question 972966
I'll do the first one to get you started.


Problem: <font color="blue">jay took a quiz with 20 question. For every correct answer, he was awarded 3 points .for every wrong answer,2 points were deducted. If jay scored zero points for the quiz, how many questions did jay answer correctly?</font>

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Solution:


x = number of correct answers
y = number of incorrect answers


There are 20 questions total, so x+y = 20. Solve for y to get y = 20-x

He gets 3 points per correct question and loses 2 points for each one he gets wrong. So in total, he has 3x+(-2y) = 3x-2y points. At the end of the day, he scored 0 points, which means we know 3x-2y = 0


Use the two equations to solve for x


3x-2y = 0
3x-2(20-x) = 0 ... replace y with 20-x
3x-40+2x = 0
5x-40 = 0
5x = 40
x = 40/5
x = 8


Use this to find y


y = 20-x
y = 20-8 ... plug in x = 8
y = 12


Therefore, x = 8 and y = 12


Recall above that I made "x = number of correct answers", so because x = 8, this means Jay got 8 questions correct.


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Question: <font color="blue">If jay scored zero points for the quiz, how many questions did jay answer correctly? </font>
Answer: <font color="red">8 questions</font> (12 questions incorrectly)