Question #d3d11

1 Answer
Aug 8, 2017

Answer:

The father is 24 years old, and the son is 6 years old.

Explanation:

Let x represent the son's age.
Let y represent the man's age.

Make two equations:

(1) The man's age is equal to four times his son's age:

#y = 4x#

(2) In three years the man's age will be #y + 3#.
In three years the son's age will be #x + 3#.
In three years the man's age will be equal to three times his son's age.

#y + 3 = 3 (x+3)#

Expand the second equation:

#y + 3 = 3 (x+3)#

#y + 3 = 3x+9#

Equate the two equations:

Since #y = 4x#, you can replace the #y# in the second equation with #4x#

#y + 3 = 3x+9#

#4x + 3 = 3x+9#

Simplify the equation:

#4x + 3 = 3x+9#

#4x-3x+3= 9#

#4x-3x=9-3#

#x=6#

Substitute this value into the first equation:

#y = 4x#

#y = 4(6)#

#y = 24#

Therefore the son's age #(x)# is 6 years and the man's age #(y)# is 24 years.