# 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.

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## Comments 20 comments

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!

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.

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.

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!

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!

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

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...

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thanks for you

I NEED HELP

i like it..

way klaro

ang galing mo

very interesting...

Thanks

oo nga very interestining

it is not at all nice

20