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Michael is 3 times as old as Brandon. 18 years ago, Michael was 9 times as old as Brandon. How old is Michael now?

Michael is \(3\) times as old as Brandon. \(18\) years ago, Michael was \(9\) times as old as Brandon.\newlineHow old is Michael now?

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Full solution

Q. Michael is \(3\) times as old as Brandon. \(18\) years ago, Michael was \(9\) times as old as Brandon.\newlineHow old is Michael now?
  1. Denoting Michael and Brandon: Let's denote Michael's current age as MM and Brandon's current age as BB. According to the problem, Michael is 33 times as old as Brandon, which gives us our first equation:\newlineM=3BM = 3B
  2. Equation 11: Michael is 33 times as old as Brandon: The problem also states that 1818 years ago, Michael was 99 times as old as Brandon. We can express this with a second equation:\newlineM−18=9(B−18)M - 18 = 9(B - 18)
  3. Equation 22: 1818 years ago, Michael was 99 times as old as Brandon: Now we have a system of two equations:\newline11) M=3BM = 3B\newline22) M−18=9(B−18)M - 18 = 9(B - 18)\newlineWe can substitute the value of MM from the first equation into the second equation to find BB.\newline3B−18=9(B−18)3B - 18 = 9(B - 18)
  4. System of equations: Let's solve for BB:3B−18=9B−1623B - 18 = 9B - 162Now, we'll move all terms involving BB to one side and constants to the other side:3B−9B=−162+183B - 9B = -162 + 18−6B=−144-6B = -144
  5. Substituting MM into Equation 22: Divide both sides by −6-6 to find BB:\newlineB=−144−6B = \frac{-144}{-6}\newlineB=24B = 24\newlineSo, Brandon is currently 2424 years old.
  6. Solving for Brandon's age: Now that we know Brandon's age, we can find Michael's age using the first equation:\newlineM=3BM = 3B\newlineM=3×24M = 3 \times 24\newlineM=72M = 72\newlineMichael is currently 7272 years old.

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