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Math Help - Percentages stumped me.

  1. #1
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    Percentages stumped me.

    G'day from Australia. Cody here.
    this one stumped me, how may I approach it please?
    "a maths exam contained only 2 questions, prob 1 solved by 70%
    prob 2 by 60% of students,every pupil solved at least 1 problem.
    9 students solved both problems. How many pupils took the exam?
    Thank you kindly for any assistance.
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  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Quote Originally Posted by cody94 View Post
    G'day from Australia. Cody here.
    this one stumped me, how may I approach it please?
    "a maths exam contained only 2 questions, prob 1 solved by 70%
    prob 2 by 60% of students,every pupil solved at least 1 problem.
    9 students solved both problems. How many pupils took the exam?
    Thank you kindly for any assistance.
    Let P be the number of pupils that took the exam.

    We know that 0.7P pupils got question 1 correct and that 0.6P got question 2 correct. Since 9 students go both problems correct they are counted twice (once for question 1 and again for question 2). So we have overcounted by 9 students. So we get the equation

    0.7P+0.6P-9=P \iff 0.3P=9 \iff P=30

    So the number of pupils that took the exam was 30.

    I hope this helps. Good luck.
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  3. #3
    Eater of Worlds
    galactus's Avatar
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    Hello Cody. This is Cody

    Since 70% solved problem 1 and 60% solved problem 2 and 9 solved both, then this appears to be a P(A)+P(B)-P(A and B)

    Let P(A)=.70 and P(B)=.60

    Then A and B=9

    So, 9 must be the portion that is the 30 %

    9 is 30% of what number?. 9/.30=
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  4. #4
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    Thank you very much, Galactus and MTset,
    I can see both avenues now.
    The "overcounting by 9" was the trick for me.
    appreciate you time.
    Cody.
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