# Thread: what does p+q equal?

1. ## what does p+q equal?

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

a 9
b 10
c 12
d 15
e 20

2. Hello,
Originally Posted by foreverbrokenpromises
If $\displaystyle pq$ = 4, and $\displaystyle p^2q + pq^2 +p + q$= 60, then $\displaystyle p+q$ equals??

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

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

Finish it

3. Originally Posted by foreverbrokenpromises
If $\displaystyle pq$ = 4, and $\displaystyle p^2q + pq^2 +p + q$= 60, then $\displaystyle p+q$ equals??

a 9
b 10
c 12
d 15
e 20
$\displaystyle p^2q + pq^2 +p + q= 60 \implies pq(p+q) +(p + q)= 60$ $\displaystyle \implies (pq+1)(p+q) = 60 \implies 5 (p+q) = 60 \implies \text{c}$

4. ANOTHER WAY:

Solve for p

$\displaystyle p=\frac{4}{q}$

then substitute this $\displaystyle \frac{4}{q}$

into the equation

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

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