Question 134832
Let x=annie's age now
And let y=Sean's age now

Now we are told that:

x+5=(1/2)(y+5) or
x+5=y/2 + 5/2  multiply each side by 2

2x+10=y+5 subtract 10 and also y from each side
2x-y+10-10=y-y-10+5  collect like terms
2x-y=-5------------------------------------------------eq1

We are also told that:

(1/2)(x+12)=(1/3)(y+12)
x/2 + 6=y/3 + 4  multiply each side by 6
3x+36=2y+24  subtract 2y and also 36 from each side

3x+36-36-2y=2y-2y-36+24  collect like terms

3x-2y=-12----------------------------------------------eq2

Multiply eq1 by 2:

4x-2y=-10-------------eq1a
subtract this from eq2

-x=-2 divide each side by -1

x=2 years old-----------------annie's age now

substitute x=2 into eq2
3*2-2y=-12

6-2y=-12  subtract 6 from each side
6-6-2y=-12-6  collect like terms
-2y=-18  divide both sides by -2

y=9 years old ------------------------Sean's age now


CK
2+5=(1/2)(9+5)
7=7
also
(1/2)(2+12)=(1/3(9+12)
7=7


Hope this helps----ptaylor