what does p+q equal?

**foreverbrokenpromises** · May 24th 2009, 01:37 PM

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

**Moo** · May 24th 2009, 01:40 PM

Hello,

Originally Posted by foreverbrokenpromises

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

**Isomorphism** · May 24th 2009, 01:40 PM

Originally Posted by foreverbrokenpromises

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

$p^2q + pq^2 +p + q= 60 \implies pq(p+q) +(p + q)= 60$ $\implies (pq+1)(p+q) = 60 \implies 5 (p+q) = 60 \implies \text{c}$

**VonNemo19** · May 24th 2009, 01:44 PM

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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