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Michael is 12 years older than Brandon. Seventeen years ago, Michael was 4 times as old as Brandon. How old is Brandon now?

Michael is \(12\) years older than Brandon. Seventeen years ago, Michael was \(4\) times as old as Brandon.\newlineHow old is Brandon now?

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Full solution

Q. Michael is \(12\) years older than Brandon. Seventeen years ago, Michael was \(4\) times as old as Brandon.\newlineHow old is Brandon now?
  1. Define current ages of Michael and Brandon: Let's define the current ages of Michael and Brandon as MM and BB, respectively. According to the problem, Michael is 1212 years older than Brandon.\newlineSo, we can write the first equation as:\newlineM=B+12M = B + 12
  2. Equation 11: Michael is 1212 years older than Brandon: Seventeen years ago, Michael's age was M−17M - 17 and Brandon's age was B−17B - 17. According to the problem, at that time, Michael was 44 times as old as Brandon.\newlineSo, we can write the second equation as:\newlineM−17=4(B−17)M - 17 = 4(B - 17)
  3. Equation 22: Michael was 44 times as old as Brandon 1717 years ago: Now we have a system of two equations:\newline11) M=B+12M = B + 12\newline22) M−17=4(B−17)M - 17 = 4(B - 17)\newlineWe can substitute the value of MM from the first equation into the second equation to find BB.\newlineB+12−17=4B−4×17B + 12 - 17 = 4B - 4 \times 17\newlineB−5=4B−68B - 5 = 4B - 68
  4. Substitute MM from Equation 11 into Equation 22: Next, we solve for BB by rearranging the terms:\newlineB−4B=−68+5B - 4B = -68 + 5\newline−3B=−63-3B = -63\newlineB=−63−3B = \frac{-63}{-3}\newlineB=21B = 21
  5. Solve for B: Now that we have the value of B, we can find M using the first equation:\newlineM = B + 1212\newlineM = 2121 + 1212\newlineM = 3333

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