Question

Ric is half Paul's age. Tom is 2 years younger than Paul. The sum of all their ages is 33 years Show all working clearly to find Ric's age​

Answer 1

Ric is 7 years old.

Explanation:

Choose variables for everyone's ages. I'll choose
`r` for Ric's age,
`p` for Paul's age, and
`t` for Tom's age.

Since Ric's age is half of Paul's age, we can write this equation:

`r=(1)/(2)p`

Since Tom is two years younger than Paul, we can write this equation:

`t=p-2`

Since the sum of all their ages is 33 years, we can write this equation:

`r+p+t=33`

Since we know
`t` and
`r` in terms of
`p`, we can replace them in the equation above as follows:

`r+p+t=33\\((1)/(2)p)+p+(p-2)=33`

Now we can solve for
`p` to find
`r` later:

`((1)/(2)p)+p+(p-2)=33\\(5)/(2)p-2=33\\(5)/(2)p=35\\5p=70\\p=14`

Now that we know that
`p=14`, we can substitute 14 for
`p\\` in the equation
`r=(1)/(2)p`:

`r=(1)/(2)p\\r=(1)/(2)(14)\\r=7`

Ric is 7 years old.