Question 1074749
kevin is twice as old as gabriela.
12 years ago, kevin was 6 times as old as gabriela.
how old is gabriela today?


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.