Question

Andrew is elder to Brian by 2 years. Andrew's father Frank is twiceas old as Andrew, and Brian is twice as old as his sister Sarah. If theages of Frank and Sarah differ by 40 years, then find the age ofAndrew.

Answer 1

Let "x" represent the age of Brian.

Andrew is elder than Brian by 2 years, we can symbolize his age as "x+2"

Frank is twice as old as Andrew, we can symbolize his age as "2(x+2)"

Sarah has half the age of Brian's, we can symbolize her age as "x/2"

Frank ans Sarah's ages differ by 40 years, we can symbolize this as:

$2(x+2)-\frac{x}{2}=40$

Solve the term is parenthesis

$\begin{gathered} 2x+4-\frac{1}{2}x=40 \\ 2x-\frac{1}{2}x+4=40 \\ \frac{3}{2}x=40-4 \\ \frac{3}{2}x=36 \\ x=24 \end{gathered}$

x=24 years

Andrew's age is

$x+2=24+2=26$

Andrew is 26 years old