Question

A man x years old which his son Is your years old. the sum of their age is twice the difference of their age. if the product of their age is 675. find the age of the man​

Answer 1

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

`\left \{ {x + y = 2 (x-y)} \atop {x*y=675}} \right.`

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

`\left \{ {x=3y} \atop {(3y)*y=675}} \right.`

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])