Question 996754
x = ompong's age today.
y = vongfong's age today.


ompong  is 3 years younger than vongfong.


x = y - 3


six years ago, ompong's age was 2/3 of vongfong's age.


x - 6 = 2/3 * (y - 6).


what are their present ages?


you have two equations to solve simultaneously.


they are x = y - 3 (first equation) and x - 6 = 2/3 * (y - 6) (second equation).


simplify the second equation to get:


x-6 = 2/3(y-6) becomes x-6 = 2/3 * y - 2/3 * 6


simplify further to get x-6 = 2/3 * y - 4.


the first equation tells you that x = y - 3.


you can replace x with y - 3 in the second equation because they are equivalent.


replace x in the second equation with (y - 3) to get:


(y - 3) - 6 = 2/3 * y - 4.


simplify to get:


y - 9 = 2/3 * y - 4


add 9 to both sides of this equation to get:


y = 2/3 * y + 5


subtract 2/3 * y from both sides of this equation to get:


1/3 * y = 5


multiply both sides of this equation by 3 to get:


y = 15


if y = 15, then x must be equal to 12 because x = y - 3.


you have x = 12 and y = 15.


that's their ages today.


ompong is 12.
vongfong is 15.


six years ago ompong was 6 and vongfong was 9.


6 is equal to 2/3 * 9.


solution looks good.


present ages of ompong and vongfong are 12 and 15.