Question 996754: Ompong is three years younger than VongFong. Six years ago, Ompong's age was two-thirds of VongFong's age. What are their present ages?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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