The difference between the ages of a man and his son is 20. If the man is 4 times older than his son

Mathematics

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Step-by-step solution

5 steps
  1. Define the variables.

    Let MM be the age of the man.
    Let SS be the age of the son.

  2. Formulate the equations based on the given information.

    From the first statement, "The difference between the ages of a man and his son is 20":

    M−S=20(1)M - S = 20 \quad (1)

    From the second statement, "the man is 4 times older than his son":

    M=4S(2)M = 4S \quad (2)
  3. Substitute equation (2) into equation (1).

    Substitute 4S4S for MM in equation (1):

    4S−S=204S - S = 20 3S=203S = 20
  4. Solve for SS.

    Divide both sides by 3:

    S=203S = \frac{20}{3}
  5. Solve for MM.

    Substitute the value of SS back into equation (2):

    M=4×203M = 4 \times \frac{20}{3} M=803M = \frac{80}{3}

    The age of the son is 203\frac{20}{3} years, and the age of the man is 803\frac{80}{3} years.

    Son’s age=203 years, Man’s age=803 years\boxed{\text{Son's age} = \frac{20}{3} \text{ years}, \text{ Man's age} = \frac{80}{3} \text{ years}}
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