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Kevin is 2 times as old as Gabriela. 12 years ago, Kevin was 6 times as old as Gabriela. How old is Kevin now?

Kevin is \(2\) times as old as Gabriela. \(12\) years ago, Kevin was \(6\) times as old as Gabriela.\newlineHow old is Kevin now?

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Full solution

Q. Kevin is \(2\) times as old as Gabriela. \(12\) years ago, Kevin was \(6\) times as old as Gabriela.\newlineHow old is Kevin now?
  1. Define ages of Kevin and Gabriela: Let's define the current ages of Kevin and Gabriela as KK and GG, respectively. According to the problem, Kevin is 22 times as old as Gabriela.\newlineFirst equation: K=2GK = 2G
  2. First equation: 1212 years ago, Kevin's age was K−12K - 12 and Gabriela's age was G−12G - 12. According to the problem, at that time, Kevin was 66 times as old as Gabriela.\newlineSecond equation: K−12=6(G−12)K - 12 = 6(G - 12)
  3. Second equation: Now we have a system of two equations:\newline11) K=2GK = 2G\newline22) K−12=6(G−12)K - 12 = 6(G - 12)\newlineWe can substitute the value of KK from the first equation into the second equation to find GG.\newline2G−12=6(G−12)2G - 12 = 6(G - 12)
  4. Substitute KK into second equation: Let's solve for GG:
    2G−12=6G−722G - 12 = 6G - 72
    Add 1212 to both sides:
    2G=6G−602G = 6G - 60
  5. Solve for G: Now, subtract 6G6G from both sides to get GG on one side:\newline2G−6G=−602G - 6G = -60\newline−4G=−60-4G = -60
  6. Find Kevin's current age: Divide both sides by ext{−4-4} to solve for GG: \newlineG=−60−4G = \frac{-60}{-4}\newlineG=15G = 15
  7. Find Kevin's current age: Divide both sides by −4-4 to solve for GG:
    G=−60−4G = \frac{-60}{-4}
    G=15G = 15Now that we have Gabriela's current age, we can find Kevin's current age using the first equation:
    K=2GK = 2G
    K=2×15K = 2 \times 15
    K=30K = 30

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