# Solving Age Problems

Solving Age Problems

One of the most popular applications of linear equations is solving age problems. In this hub I present three word problems of this sort with their complete solution. Hope you will enjoy this hub.

Problem Number One :

A mother’s age is five years greater than twice her son’s age as of the present. Fifteen years sgo the mother’s age was six times her son’s age. What are the present ages of the mother and the son ?

Solution :

Representation:

Their present ages:

Let X = Son’s age

2X + 5 = Mother’s age

Their ages 15 years ago:

X – 15 = Son’s age

2X + 5 -15 = 2X -10 = Mother’s age

Working Equation :

2X – 10 = 6( X – 15 )

2X - 10 = 6X – 90

90 – 10 = 6X – 2X

80 = 4X

80/4 = 4X/4

20 = X

X = 20

2X + 5 = 2(20) + 5 = 45

The mother is 45 years old and the son is 20 years old as of the present.

Problem Number Two :

A grandpa’s age is five times his grandson’s age. Ten years from now the grandpa’s age will be three times his grandson’s age. Find their present ages.

Solution :

Representation :

Their present ages:

Let X = grandson’s age

5X = grandpa’s age

Their ages ten years from now

X + 10 = grandson’s age

5X + 10 = grandpa’s age

Working equation :

5X + 10 = 3 (X + 10 )

5X + 10 = 3X + 30

5X – 3X = 30 – 10

2X = 20

2X/2 = 20/2

X = 10

5X = 50

Grandpa’s age is 50 while his grandso’s age is 10 years as of the present.

Problem Number Three :

Fred is three years older than his sister Mary who is eleven years old as of the present.. In how many years will Mary’s age be six-sevenths of Fred’s present

age?

Solution :

Representation:

Let X = the number of years Mary’s age will be 6/7 of her brother’s age

Their ages after X years

11 + X = Mary’s age in X years

14 + X = Fred’s age in X years

Working Equation :

11 + X = 6/7 ( 14 + X )

7(11 + X) = (6/7(14 + X )) 7

77 + 7X = 6(14) + 6X

77 + 7X = 84 + 6X

7X – 6X = 84 – 77

X = 7 years.

Mary’s age will be 6/7 of her brother’s age in seven years.

## More by this Author

fred allen 5 years ago from Myrtle Beach SC

Thanks for putting me in this brainiac hub! For the record, my sister's name is Michelle!

You are as smart as you are beautiful inside and out!

Dave Mathews 5 years ago from NORTH YORK,ONTARIO,CANADA

I am totally befuddled with math problems. In arithmatic I thought that 1 plus 1 should be 11, but uh uh! its 2

Hi Ate Cristina, how's things?

Brother Dave.

cristina327 5 years ago from Manila Author

Hi Fred allen thank you for appreciating this hub. Your visit and comments are much appreciated. Blessings to you.

cristina327 5 years ago from Manila Author

Hi Dave Matthews thanks for dropping by. By God's grace I am still alright. God is still faithful in sustaining me. Blessings to you.

jayb23 5 years ago from India

Cristna U made me nostalgic. These problems make me remember my school days :-) Some more stuff on these linear equations will be great. Keep up d good work.

cristina327 5 years ago from Manila Author

Hi jayb23 it is nice to hear from you again. Thanks for dropping by. Your visit and comment is much appreciated.

Judicastro 5 years ago from birmingham, Alabama

Hi Cristina hope all is well! Thought I'd stop by and see how your hub was adding up (-: looks like you are on the positive side of the equation!! Bless you sister!

DeBorrah K. Ogans 5 years ago

Cristina, Interesting... I see that you are not only spiritually deep but smart! lol May our Father continue to BLESS and KEEP YOU!

Thank you for sharing, In HIS, Love, Peace & Blessings!

cristina327 5 years ago from Manila Author

Hi Judicastro it is great to hear from you again. Thank you for dropping by. Your visit and comment is much appreciated. Blessings to you.

cristina327 5 years ago from Manila Author

Hi DeBorrah K. Ogans it is very encouraging to read your comment. Thank you for gracing this hub. Your visit and comment is much appreciated. Blessings to you always.

Ken 5&9 5 years ago

hi aten cristina...im from philippines..thanks for sharing these age problems...it helps a lot...^_^ ...God bless.

farmvillefcu 4 years ago

Wow this is one kind of problem in algebra which I really like. The age Problem. Thank you for posting. I got also mine, a little bit simple:

http://hubpages.com/education/Solving-Age-Problem...

or if you want to relax: http://www.farmvillefcu.com/

star 4 years ago

thanks for you

BOB 4 years ago

I NEED HELP

ann 3 years ago

i like it..

olver 3 years ago

way klaro

fuck 3 years ago

ang galing mo

youcanwin 3 years ago

very interesting...

Thanks

gurl non love life 3 years ago

oo nga very interestining

anu 2 years ago

it is not at all nice