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Pablo is four yrs older than his sister. The product of their ages is 21. Determine their aged.

Mathematics

ScanSolve AI Answer

Answer

Faith: 3 years, Nabil: 7 years\text{Faith: 3 years, Nabil: 7 years}

Step-by-step solution

6 steps

Here's the solution to the problem:

  1. Define variables for the ages.

    Let FF be Faith's age.
    Let NN be Nabil's age.

  2. Formulate equations based on the given information.

    "Nabil is four years older than his sister Faith":

    N=F+4N = F + 4

    "The product of their ages is 21":

    N×F=21N \times F = 21
  3. Substitute the first equation into the second to form a quadratic equation.

    Substitute N=F+4N = F + 4 into N×F=21N \times F = 21:

    (F+4)F=21(F + 4)F = 21 F2+4F=21F^2 + 4F = 21 F2+4F−21=0F^2 + 4F - 21 = 0
  4. Solve the quadratic equation for Faith's age.

    Factor the quadratic equation:

    (F+7)(F−3)=0(F + 7)(F - 3) = 0

    This gives two possible solutions for FF:

    F=−7orF=3F = -7 \quad \text{or} \quad F = 3

    Since age cannot be negative, Faith's age is F=3F = 3 years.

  5. Determine Nabil's age.

    Using the equation N=F+4N = F + 4:

    N=3+4N = 3 + 4 N=7N = 7

    Nabil's age is 7 years.

  6. State their ages.

    Faith's age is 3 years and Nabil's age is 7 years.

    Faith: 3 years, Nabil: 7 years\text{Faith: 3 years, Nabil: 7 years}
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