Example Today, the age of Robert is the same as four times the age of Sarah. After 14 years, the age of Robert will be double the age of Sarah. Find their present ages.

Solution :

Let the present age of Sarah be 'x ' years.

Therefore, Robert’s present age is 4 x years.

Setting up an equation as:

4 x + 12 = 2 x + 24

4 x - 2 x = 24 - 12

2 x = 12

x = 6

Therefore, Sarah’s present age is 6 years

Robert’s present age is 4 (6) = 24 years

Check: 4 ( 6 ) = 24 and 24 + 12 = 2 ( 6 + 12 )

36 = 36

Example The sum of the ages of Phil and his mother is 60 years . Five years ago, the age of Phil’s mother was four times his age . Find their present ages.

Solution : Let ’ x years ’ be Phil’s present age.

The sum of his age and his mother’s is 60 years.

x + (Mother’s age) = 60

Mother’s present age is (60 - x) years

Setting up an equation as -

55 - x = 4 x - 20

55 + 20 = 4 x + x

5 x = 75

x = 15

Therefore, Phi’s present age is 15 years.

Mother’s present age is 45 years.

Check : 15 + 45 = 60

and 45 - 5 = 4 ( 15 - 5 )

40 = 40

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Index

9.1 - Definition and Solving Techniques
9.2 - Use of Simultaneous Linear Equations

Chapter 1