Given:
A grandfather is 9 times older than his granddaughter.
In 8 years the grandfather will be 5 times older than his granddaughter.
To find:
The present age of grandfather and granddaughter.
Solution:
Let x be the present age of granddaughter.
Then, present age of grandfather = 9x
After 8 years,
Age of granddaughter = x+8
Age of grandfather = 9x+8
In 8 years the grandfather will be 5 times older than his granddaughter.
[tex]9x+8=5(x+8)[/tex]
[tex]9x+8=5x+40[/tex]
Isolate variable terms.
[tex]9x-5x=-8+40[/tex]
[tex]4x=32[/tex]
Divide both sides by 4.
[tex]x=8[/tex]
Now,
Present age of granddaughter = 8
Present age of grandfather = 9(8) = 72
Therefore, the present age of granddaughter is 8 years and present age of grandfather is 72 years.
