The age of a boy is one third of his father's age. If the sum of their ages is 80 years, find the age of each of them.

Answer: The father's age is 60, and the boy's age is 20.

Solution: Let the father's age be [tex]x[/tex] years. Then, the boy's age is [tex]\frac{x}{3}[/tex] years. The sum of their ages is given by:

[tex]x + \frac{x}{3} = 80[/tex]

Solving for [tex]x[/tex]:

Multiply every term by 3 to eliminate the fraction:

[tex]3x + x = 240[/tex]

Combine like terms:

[tex]4x = 240[/tex]

Divide by 4:

[tex]x = 60[/tex]

So, the father's age is 60 years, and the boy's age is:

[tex]\frac{60}{3} = 20[/tex]

Thus, the boy is 20 years old.

The father's age is 60 years and the boy's age is 20 years. These ages were determined by setting up and solving an equation based on the information given in the question.

Explanation:

The question says the age of a boy is one-third of his father's age. This means if we represent the father's age as 'x', then we can say the boy's age is 'x/3'. The question also tells us that the sum of their ages is 80 years. This translates to an equation like 'x + x/3 = 80'.

To solve the equation, we should first get rid of the fraction by multiplying every term by 3. This gives us '3x + x = 240'. Simplifying it gives '4x = 240'. Dividing each side by 4 gives us 'x = 60'.

So, the father's age is 60 years. Because the boy's age is one-third of his father's, we divide the father's age by 3 to get 'the boy's age is 20 years'.

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