x = Heather's age NOW
x - 2 = her age 2 years ago
x - 3 = her age 3 years ago
[tex]\frac{1}{2}(x-2)+\frac{1}{3}(x-3)=20 [/tex]
The Least Common Multiple of 2 and 3 is 6. Multiply both sides by 6.
[tex]6\cdot\frac{1}{2}(x-2)+6\cdot\frac{1}{3}=6\cdot20 \\3(x-2)+2(x-3)=120 \\ 3x-6+2x-6=120 \\ 5x-12=120 \\ 5x=132 \\ x=\frac{132}{5}=26.4 [/tex]
