SOLUTION: Tommy is 4 years older than his sister, Candace. The product of their ages is 96. How old is Tommy?

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Question 1001375: Tommy is 4 years older than his sister, Candace. The product of their ages is 96. How old is Tommy?
Answer by MathLover1(20850) About Me  (Show Source):
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Tommy is 4 years older than his sister, Candace.
T=C%2B4....eq.1
The product of their ages is 96:
T%2AC=96
T=96%2FC....eq.2
from eq.1 and eq.2 we have

C%2B4=96%2FC
C%5E2%2B4C=96
C%5E2%2B8C-12C-96=0
%28C%5E2%2B8C%29-%2812C%2B96%29=0
C%28C%2B8%29-12%28C%2B8%29=0
%28C-8%29%28C%2B12%29+=+0
solutions:
if %28C-8%29+=+0=>C=8
if %28C%2B12%29+=+0=>C=-12...disregard negative solution, we are looking for age
so, C=8=>Candace
T=8%2B4....eq.1
T=12.... Tommy is 12 years old