Let's take as x and y the age of the man and of his son
We will do a system, so we can satisfy all the request:
1. sum of ages = 2 (difference)
2. product = 675
[tex]\left \{ {x + y = 2 (x-y)} \atop {x*y=675}} \right.[/tex]
semplify the first equation
x + y = 2x -2y
now let's choose one of the incognite (x) and we solve for it
x - 2x = - 2y - y
- x = - 3y
x = 3y
Let's substitute this solution in the second equation
[tex]\left \{ {x=3y} \atop {(3y)*y=675}} \right.[/tex]
note: x = 3y, so in the second equation x * y = 3y * y
Now let's solve the second equation
3y * y = 675
3y² = 675
y² = 675 / 3 =
y² = 225
y = 15
Son's age is 15
Man's age is 15 * 3 = 45 (See the first equation [x = 3y])
