Answer: Kevin is 30 years old today and Gabriela is 15 years old today.
Step-by-step explanation: let k = kevin's age today.
let b = gabriela's age today.
k = 2g
this means kevins age is two time gabriela's age today.
12 years ago, kevin was 6 times as old as gabriela was 12 years ago.
kevin's age 12 years ago was k - 12.
gabriela's age 12 hears ago was g - 12.
(k - 12) = 6 * (g - 12)
this means that kevin's age 12 years ago was 6 times gabriela's age 12 years ago.
so, you have 2 equations.
k = 2g
(k - 12) = 6 * (g - 12)
these 2 equations have to be solved simultaneously because the same answer has to apply to both equations and not just one of them.
since k = 2g from the first equation, then replace k in the second equation with 2g.
you get (2g - 12) = 6 * (g - 12)
now this equation can be solved for g.
simplify this equation to get 2g - 12 = 6g - 72
subtract 2g from both sides of the equation and add 72 to both sides of the equation to get 60 = 4g.
solve for g to get g = 60/4 = 15.
if g = 15, then k = 2g = 30.
your answer is that kevin is 30 years old today and gabriela is 15 years old today.
12 years ago, kevin would have been 30 - 12 = 18.
12 years ago, gabriela would have been 15 - 12 = 3.
12 years ago kevin would have been 18 / 3 = 6 times as old as gabriela was 12 years ago.
this confirms the answer is correct because all the problem statements have been satisfied.
