SOLUTION: 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?

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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