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Math Help - Algebra problem

  1. #1
    Senior Member
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    Algebra problem

    I am completely stuck on this, please explain clearly.

    Many thanks


    In this question x * y means (x+2y)/3 if x < y, and (2x + y)/3 if x is larger or equal to y.

    a) Find the value of

    i) 5 * 8
    ii) 8 * 5


    b) Solve

    iii) x * 7 = 8
    iv) x * (x-1) = 4 2/3 (that's 4 followed by 2/3 as a fraction)

    c) In terms of p and q, find the possible values of (p * q) *p, explaining carefully how you choose which calculations to make.
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  2. #2
    Super Member Quacky's Avatar
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    In this question x * y means \frac{x+2y}{3} if x < y, and \frac {2x+y}{3} if x is larger or equal to y.

    a) Find the value of

    i) 5 * 8

    So x = 5 and y = 8. Clearly, x<y, so just substitute the values 'x=5' and 'y=8' into the first equation to give:

    \frac{5+(2)(8)}{3}

    This simplifies to give an answer of 7.

    Can you apply this to part ii)?

    Then for part b) iii)
    We know that y=7 and the answer is 8. Substituting that into the original equation:
    \frac{x+2y}{3}

    Gives:

    \frac{x+2(7)}{3}=8
    \frac{x+14}{3}=8
    x+14=24
    x=10

    As this value of x is greater than our value of y, however, this is incorrect as we can only use this equation 'if x < y'

    So you'll have to substitute the values into the second equation.

    \frac {2x+(7)}{3}=8
    2x+7=24
    2x=17
    x=\frac{17}{2}=8.5

    Can you apply this to part ii?

    FInally, part c. I don't understand part c as it seems to me that there could be almost infinite values for that equation. Is it not just trial and error?
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  3. #3
    Member u2_wa's Avatar
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    Quote Originally Posted by Natasha1 View Post
    I am completely stuck on this, please explain clearly.

    Many thanks


    In this question x * y means (x+2y)/3 if x < y, and (2x + y)/3 if x is larger or equal to y.


    c) In terms of p and q, find the possible values of (p * q) *p, explaining carefully how you choose which calculations to make.
    I think there are two possibilities:

    1. P<q and (P * q)>p
    2. p>q and (p * q)<p

    1. [p * q] * p = [(p+2q)/3]* p {In this case I have used ,(x+2y)/3 if x < y, by letting p=x and q=y}
    = [2([(p+2q)/3])+p]/3. { In this case I have used, (2x + y)/3 if x is larger or equal to y, by substituting p=y and [(p+2q)/3] = x}
    you can try the second part!!
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