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Question 972966: 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?
Gordon had 3 times as many picture cards as hennery. Ivan had twice as many picture cards as Gordon. If they had a total of 90 picture cards, how many more picture cards did Ivan have than henry?
thank you
Found 3 solutions by jim_thompson5910, josgarithmetic, macston:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! I'll do the first one to get you started.
Problem: 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?
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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: If jay scored zero points for the quiz, how many questions did jay answer correctly?
Answer: 8 questions (12 questions incorrectly)
Answer by josgarithmetic(39616) (Show Source):
You can put this solution on YOUR website! t for correct answers; add 3.
f for wrong answers; subtract 2.
Twenty questions, score of 0.
 .
You should analyze and formulate that system, and therefore understand that system. Solving for t and f is something you already learned. Suggestion: Start with Elimination method, using first equation as  .
Answer by macston(5194)  (Show Source):
You can put this solution on YOUR website! .
PART 1: QUIZ
C=correct answers; W=wrong answers
C+W=20
W=20-C Use this to substitute for W.
.
3C-2W=0 Substitute for W.
3C-2(20-C)=0
3C-40+2C=0
5C=40
C=8 Jay answered 8 questions correctly.
CHECK:
W=20-C=20-8=12 Jay answered 12 questions incorrectly.
3C-12W=0
3(8)-2(12)=0
24-24=0
0=0
.
.
PART 2:CARDS
.
H=number of Henry's cards; G=number of Gordon's cards=3H;
I=number of Ivan's cards=2G=6H
.
H+G+I=90 Substitute for G and I
H+3H+6H=90
10H=90
H=9 Henry had 9 cards.
I=6H=6(9)=54 Ivan had 54 cards.
G=3H=3(9)=27
CHECK:
H+G+I=90
9+27+54=90
90=90
.
I-H=54-9=45
ANSWER: Ivan had 45 more cards than Henry.
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