## Sep 21, 2009

### Age Problems - Equations in single variable - Algebra

This worksheet is based on age word problems which come under equations in one variable. Intermediate Algebra, Algebra – I and Algebra – II students can practice these questions.
1. Miguel is 46 years old. He is 4 years older than thrice his son’s age. Find the age of his son.
Solution:
Age of Miguel = 46 years
Age of Son       = x years
So, 46               = 4 +3x
Subtracting 4 on both sides,
42   =3x
Dividing by 3 on both sides,
X =14
Therefore, the Son is 14 years old.
2. Pete, Bryan and Philip are cousins. Pete’s age is one-third of Bryan and Philip is five years elder than Bryan. If the sum of the age of the cousins is 40, find the ages of each.
Solution:
From the statement,
Age of Bryan= x
Age of Pete   =x/3
Age of Philip = x+5
Sum of the ages=40.
X/3 + x+x+5= 40
(7x+15)/3 =40
Multiplying by 3 on both sides,
7x +15=120
Subtracting 15 on both sides,
7x=105
Dividing by 7 on both sides,
X=15
Therefore, age of Pete=15/3=5
Age of Bryan                 =15
Age of Philip                  =15+5=20
3. Ana is 5 years more than Jack. The sum of their ages is 29. Find the ages of Ana and Jack.
4. Tina is 3 years younger than Tom. The ages are in the ratio 2:3. Find their ages.
5. George is 8 years more than Christopher and Ford is 2 years younger than Christopher. The sum of their ages is 60. Find the ages of George, Christopher and Ford.
6. Devon is 12 years old. His age is 2 more than half the age of Steven. Find the age of Steven.
7. Mrs. Smith is 8 years more than twice the age of his son. The ages of son is 12.Find the age of mother and find the difference between their ages.
8. Kate is 12 years old. His age is 4 times the age of Robbie. Find the age of Robbie.
9. The sum of present age of Abe and the age before 7 years is 31. Find the present age of Abe. What will be his age after 7 years?
10. George is 8 years more than Christopher and Ford is 2 years younger than Christopher. The sum of their ages is 60. Find the ages of George, Christopher and Ford.
11. Margaret is 8 years more than twice the age of his son. The age of son is 12. Find the age of mother and find the difference between their ages.
12. Miguel is 46 years old. He is 6 years older than thrice his son’s age. Find the age of his son.
13. Nick and Kane were born on consecutive years and on same date. Nick is younger.  The sum of their ages is 11. Find the age of the brothers.
14. The ages of Ashley and Mary are in the ratio 4:7. The sum of their ages is 22. Find the ages of Ashley and Mary.
15. The ages of Peter, Margaret and Jack are consecutive odd numbers. The sum of the ages of Peter and Margaret equals Jack’s age before 5 years. Find the ages of Peter, Margaret and Jack.
16. The sum of the ages of Tony and Teddy equals thrice their mother’s age. Tony is two years younger than Teddy. If the age of the mother is 42, find the ages of Tony and Teddy?
17. At present Allen is 10 years younger than Scott. Five years from now, Scott’s age will be 2 times the present age of Allen. Find the present age of Allen and Scott.
18. The present ages of Lewis and Brown are in the ratio 1:2. Three years from now, the ages will be in the ratio 3:5. Find the present ages of Lewis and Brown.

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