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Bob’s age is 15 years less than half his father’s age. In six years, his father’s age will be eleven years more than triple Bob’s age. What is his father’s age now?

Answer :

His father's age is 44 years

Step-by-step explanation:

The given is:

  • Bob’s age is 15 years less than half his father’s age
  • In six years his father’s age will be eleven years more than triple Bob’s age

We need to find his father’s age now

Assume that the Father's age is x years

∵ The father's age is x years

∵ Bob’s age is 15 years less than half his father’s age

- That means multiply x by half and subtract 15 from it

∴ Bob's age = [tex]\frac{1}{2}[/tex] x - 15

In six years

The father's age = x + 6

The Bob's age = [tex]\frac{1}{2}[/tex] x - 15 + 6 = [tex]\frac{1}{2}[/tex] x - 9

∵ In six years his father’s age will be eleven years more than

triple Bob’s age

- That means equate (x + 6) by 3 times Bob's age and add 11

to the product

∴ x + 6 = 3( [tex]\frac{1}{2}[/tex] x - 9) + 11

- Simplify the right hand side

∴ x + 6 = [tex]\frac{3}{2}[/tex] x - 27 + 11

- Add like terms in the right hand side

∴ x + 6 = [tex]\frac{3}{2}[/tex] x -16

- Subtract 6 from both sides

∴ x = [tex]\frac{3}{2}[/tex] x - 22

- Subtract [tex]\frac{3}{2}[/tex] x from both sides

∴ [tex]\frac{-1}{2}[/tex] x = -22

- Divide both sides by [tex]\frac{-1}{2}[/tex]

∴ x = 44

His father's age is 44 years

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