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Math Help - what does p+q equal?

  1. #1
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    what does p+q equal?

    If pq = 4, and p^2q + pq^2 +p + q= 60, then p+q equals??

    a 9
    b 10
    c 12
    d 15
    e 20
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  2. #2
    Moo
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    Hello,
    Quote Originally Posted by foreverbrokenpromises View Post
    If pq = 4, and p^2q + pq^2 +p + q= 60, then p+q equals??

    a 9
    b 10
    c 12
    d 15
    e 20
    p^2q+pq^2=pq(p+q)

    Hence we have (p+q)(pq+1)=60

    Finish it
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  3. #3
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    Quote Originally Posted by foreverbrokenpromises View Post
    If pq = 4, and p^2q + pq^2 +p + q= 60, then p+q equals??

    a 9
    b 10
    c 12
    d 15
    e 20
    p^2q + pq^2 +p + q= 60 \implies pq(p+q) +(p + q)= 60  \implies (pq+1)(p+q) = 60 \implies 5 (p+q) = 60 \implies  \text{c}
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  4. #4
    No one in Particular VonNemo19's Avatar
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    ANOTHER WAY:

    Solve for p

    p=\frac{4}{q}

    then substitute this \frac{4}{q}

    into the equation

    (\frac{4}{q})^2q+\frac{4}{q}q^2+\frac{4}{q}+q=60

    solve for q, reapeat the process with p, and then add 'em up!
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