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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 Michael now?

Michael is \(12\) years older than Brandon. Seventeen years ago, Michael was \(4\) times as old as Brandon.\newlineHow old is Michael 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 Michael now?
  1. Equation 11: Michael's Age: Let's denote Michael's current age as MM and Brandon's current age as BB. According to the problem, Michael is 1212 years older than Brandon, which gives us our first equation:\newlineM=B+12M = B + 12
  2. Equation 22: Michael and Brandon's Ages 1717 Years Ago: Seventeen years ago, Michael's age would have been M−17M - 17, and Brandon's age would have been B−17B - 17. The problem states that at that time, Michael was 44 times as old as Brandon. This gives us our second equation:\newlineM−17=4(B−17)M - 17 = 4(B - 17)
  3. System of Equations: 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 use substitution or elimination to solve this system. Let's use substitution since we already have MM expressed in terms of BB in the first equation.
  4. Substitution Method: Substitute the expression for M M from the first equation into the second equation:\newline(B+12)−17=4(B−17) (B + 12) - 17 = 4(B - 17) \newlineNow, let's solve for B B .
  5. Simplifying the Equation: Simplify the equation:\newlineB+12−17=4B−68B + 12 - 17 = 4B - 68\newlineCombine like terms:\newlineB−5=4B−68B - 5 = 4B - 68
  6. Isolating B: Now, let's isolate B on one side of the equation:\newlineB−4B=−68+5B - 4B = -68 + 5\newline−3B=−63-3B = -63
  7. Finding Brandon's Age: Divide both sides by −3 -3 to find B B :
    B=−63−3 B = \frac{-63}{-3}
    B=21 B = 21
    Brandon is currently 21 21 years old.
  8. Finding Michael's Age: Now that we know Brandon's age, we can find Michael's current age using the first equation:\newlineM=B+12M = B + 12\newlineM=21+12M = 21 + 12\newlineM=33M = 33\newlineMichael is currently 3333 years old.

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