AGE PROBLEM INVOLVING LINEAR EQUATIONS IN ONE VARIABLE

Celia is twice as old as Ben. Eight years ago, Celia was six times as
old as Ben. How old is each now?
 
Solution:
 
Let x= Ben’s age
2x = Celia’s age
 x - 8 = Ben’s age eight years ago
2x - 8 = Celia’s age eight years ago
2x - 8 = 6(x - 8)                - equation
2x - 8 = 6x - 48
2x - 6x = -48 + 8
- 4x = - 40
- 4      - 4
 
x = 10                   - Ben's age
 
2x = 20                - Celia's age
 
Hence, the present ages of Ben and Celia are 10 and 20 years respectively.
 
Check:
 
2(10) - 8 = 6(10 - 8)
20 - 8 = 6(2)
12 = 12