SOLUTION: Kevin is twice as old as gabriela. 12years ago,kevin was 6times as old as gabriela.how old is gabriela now?

Question 1074749: Kevin is twice as old as gabriela. 12years ago,kevin was 6times as old as gabriela.how old is gabriela now?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

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