Question #d3d11

1 Answer
Aug 8, 2017

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 = 4xy=4x

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

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

Expand the second equation:

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

y + 3 = 3x+9y+3=3x+9

Equate the two equations:

Since y = 4xy=4x, you can replace the yy in the second equation with 4x4x

y + 3 = 3x+9y+3=3x+9

4x + 3 = 3x+94x+3=3x+9

Simplify the equation:

4x + 3 = 3x+94x+3=3x+9

4x-3x+3= 94x3x+3=9

4x-3x=9-34x3x=93

x=6x=6

Substitute this value into the first equation:

y = 4xy=4x

y = 4(6)y=4(6)

y = 24y=24

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