Question

There are 6 people in Jacob’s family. Jacob’s sister is 5 years younger than he is. He has twin brothers who are 3 years older than he is. His mom is 3 times Jacob’s age, and his dad is 4 years older than his mom. The total of all the ages of all his family members is 165 years. How old is Jacob? Define a variable, write an equation, and solve the problem.

Answer 1

Jacob is
`16` years old.

Explanation:

Let the age of Jacob be
`x` years.

Jacob’s sister is
`5` years younger than he is.

So, the age of Jacob's sister be
`x-5` years.

Jacob's twin brothers are
`3` years older than he is.

So, the age of each of the twin brother be
`x+3` years.

Jacob's mom is
`3` times his age.

So, the age of Jacob's mom be
`3x` years.

Jacob's dad is
`4` years older than his mom.

So, the age of Jacob's dad be
`3x+4` years.

Now, the total of all the ages of all his family members is
`165` years.

So,
`x+x-5+x+3+x+3+3x+3x+4=165`

`\Rightarrow 10x+5=165`

`\Rightarrow 10x=165-5`

`\Rightarrow 10x=160`

`\Rightarrow x=(160)/(10)`

`\Rightarrow x=16`

Hence, Jacob is
`16` years old.