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A child is 12 years old, and his father is 32 years older. In how many years will the age of the father be 3 times the age of the child?

Respuesta :

msm555

Answer:

4 years

Step-by-step explanation:

Let's denote the number of years it takes for the father's age to be three times the child's age as [tex] x [/tex] years.

At present:

  • The child's age = 12 years
  • The father's age = [tex] 12 + 32 = 44 [/tex] years

After [tex] x [/tex] years:

  • The child's age will be [tex] 12 + x [/tex] years
  • The father's age will be [tex] 44 + x [/tex] years

According to the problem, the father's age will be three times the child's age after [tex] x [/tex] years:

[tex] 44 + x = 3(12 + x) [/tex]

Let's solve for [tex] x [/tex]:

[tex] 44 + x = 36 + 3x [/tex]

[tex] 44 - 36 = 3x - x [/tex]

[tex] 8 = 2x [/tex]

[tex] x = \dfrac{8}{2}[/tex]

[tex] x = 4 [/tex]

Therefore, it will take 4 years for the father's age to be three times the age of the child.

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