College Algebra Word Problem

Question

A man is currently 20 years older than his oldest son. His oldest son is currently two years older than his youngest son. Three years from the current time, the product of the ages of his sons will be ten more than eleven times the age of the father. What is the current age of mans youngest son? 

Answer 1

Let's say the current age of the father is M, the current age of the oldest son is O and the current age  of the youngest son is Y.

 

M= O +20  (The father is 20 years older than the oldest son)

 

O= Y +2    (the oldest son is 2 years older than his youngest brother)

 

3 years later:

 

(O+3) x (Y+3) = 10 + 11 x (M+3)

 

however, O= Y+2   and   M=O + 20  => M= Y + 2 + 20 => M=Y+22

 

replacing values:

 

(Y + 5) x (Y + 3) = 10 + 11 x (Y + 22 + 3)

 

Y² + 5Y + 3Y + 15 = 10 + 11Y + 275

 

Y² + 8Y + 15 = 11Y + 285

 

Y² - 3Y - 270 = 0  =>   applying -b +/- √(b² - 4ac)        factors are

                                                         2a

 

(Y+15)(y-18)  =>   Y= 18  and y= -15

 

Because we are talking of ages, there is no negative ages, so the answer is Y=18

 

The current age of the youngest son is 18