# Age-related Problems

If *x* = present age of a person*x* – 3 = age of the person 3 years ago*x* + 5 = age of the person 5 years from now or 5 years hence

Note:

The difference of the ages of two persons is constant at any time.

If*A* = present age of Albert and*B* = present age of Bryan

Sum of their ages 4 years ago = (*A* - 4) + (*B* - 4)

Sum of their ages 2 years hence = (*A* + 2) + (*B* + 2)

Difference of their ages = *A* - *B*

Example

Six years ago, Romel was five times as old as Lejon. In five years, Romel will be three times as old as Lejon. What is the present age of Lejon?

Solution

$R$ = present age of Romel

$L$ = present age of Lejon

Six years ago

$R - 6 = 5(L - 6)$

$R - 6 = 5L - 30$

$R = 5L - 24$

Five years from now (in five years)

$R + 5 = 3(L + 5)$

$R + 5 = 3L + 15$

$R = 3L + 10$

Substitute *R* = 5*L* - 24

$5L - 24 = 3L + 10$

$2L = 34$

$L = 17 \, \text{ yrs old}$ *answer*