A is elder to B by two years. A's father F is twice as old as A and B is twice as old as his sister S. If the ages of the father and the sister differs by 40 years, find the age of A?

1 Answer
Sep 3, 2015

Answer:

#A# is 26 years old.

Explanation:

The idea here is that you can use the information given to you to write four equations with four unknows, #A#, #B#, #C#, and #D#.

So, you know that #A# is two years older than #B#, which means that you can write

#A = B + 2 " "color(blue)((1))#

You also know that #A#'s father, #F#, is twice as old as #A#

#F = 2 * A" "color(blue)((2))#

The same can be said for #B# and his sister #S#

#B = 2 * S" "color(blue)((3))#

FInally, you know that the difference between the ge of the father nad the age of the sister is 40 years old, so you can write

#F - S = 40" "color(blue)((4))#

Now you can replace #F# from equation #color(blue)((2))# into equation #color(blue)((4))# and #B# from equation #color(blue)((3))# into equation #color(blue)((1))# to write

#{(A = 2S + 2), (2A - S = 40) :}#

Replace the value of #A# from the first equation into the second one to get

#2 * (2S + 2) - S = 40#

#4S - S + 4 = 40#

#3S = 36 implies S = 36/3 = 12#

This means that the age of #A# is

#A = 2 * S + 2#

#A = 2 * 12 + 2 = color(green)(26)#