Question 1001375

Tommy is {{{4}}} years older than his sister, Candace. 

{{{T=C+4}}}....eq.1

The product of their ages is {{{96}}}: 

{{{T*C=96}}}

{{{T=96/C}}}....eq.2

from eq.1 and eq.2 we have


{{{C+4=96/C}}}

{{{C^2+4C=96}}}

{{{C^2+8C-12C-96=0}}}

{{{(C^2+8C)-(12C+96)=0}}}

{{{C(C+8)-12(C+8)=0}}}

{{{(C-8)(C+12) = 0}}}

solutions:

if {{{(C-8) = 0}}}=>{{{C=8}}}

if {{{(C+12) = 0}}}=>{{{C=-12}}}...disregard negative solution, we are looking for age

so, {{{C=8}}}=>Candace

{{{T=8+4}}}....eq.1
{{{T=12}}}.... Tommy is {{{12}}} years old