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

Answer:

Jacob is $16$ years old.

Step-by-step 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, $x+x-5+x+3+x+3+3x+3x+4=165$

$\Rightarrow 10x+5=165$

$\Rightarrow 10x=165-5$

$\Rightarrow 10x=160$

$\Rightarrow x=\frac{160}{10}$

$\Rightarrow x=16$

Hence, Jacob is $16$ years old.