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Michael is 4 times as old as Brandon and is also 27 years older than Brandon. How old is Michael?

Michael is \(4\) times as old as Brandon and is also \(27\) years older than Brandon.\newlineHow old is Michael?

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Full solution

Q. Michael is \(4\) times as old as Brandon and is also \(27\) years older than Brandon.\newlineHow old is Michael?
  1. Equation 11: Michael's age in terms of Brandon's age: Let's denote Michael's age as MM and Brandon's age as BB. According to the problem, Michael is 44 times as old as Brandon. We can write this as an equation:\newlineM=4BM = 4B
  2. Equation 22: Michael's age in terms of Brandon's age and the age difference: The problem also states that Michael is 2727 years older than Brandon. We can write this as another equation:\newlineM=B+27M = B + 27
  3. System of Equations: Now we have a system of two equations with two variables:\newline11) M=4BM = 4B\newline22) M=B+27M = B + 27\newlineWe can solve this system by setting the two expressions for MM equal to each other since they both represent Michael's age.\newline4B=B+274B = B + 27
  4. Setting the expressions for Michael's age equal: To find the value of B, we will subtract B from both sides of the equation:\newline4B−B=B+27−B4B - B = B + 27 - B\newline3B=273B = 27
  5. Solving for Brandon's age: Now we divide both sides by 33 to solve for BB:3B3=273\frac{3B}{3} = \frac{27}{3}B=9B = 9
  6. Substituting Brandon's age to find Michael's age: Now that we have Brandon's age, we can find Michael's age by substituting BB back into one of the original equations. Let's use the second equation M=B+27M = B + 27:\newlineM=9+27M = 9 + 27
  7. Calculating Michael's age: Calculate Michael's age: M=36M = 36

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