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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