Question

One half of Heather's age two years ago from now plus one-third of her age three years ago is twenty years. How old is she now?

Answer 1

x = Heather's age NOW
x - 2 = her age 2 years ago
x - 3 = her age 3 years ago


`(1)/(2)(x-2)+(1)/(3)(x-3)=20`

The Least Common Multiple of 2 and 3 is 6. Multiply both sides by 6.


`6\cdot(1)/(2)(x-2)+6\cdot(1)/(3)=6\cdot20 \\3(x-2)+2(x-3)=120 \\ 3x-6+2x-6=120 \\ 5x-12=120 \\ 5x=132 \\ x=(132)/(5)=26.4`