Question

There are 4 generations. Daughter, mother, grandma, and great-grandma. The daughter is 44 less than the grandma's age. The great-grandma is 22 more than the grandma's age. The mother is 80 less than twice the grandma's age. Together they have lived 193 years. How old is each lady?

Answer 1

Answer:

Age of Grandma = 59 years.

Age of great Grandma = 81 years

Ages of Mother = 38 years

Age of Daughter = 15 years

Step-by-step explanation:

Given:

Total years they all lived = 193

We need to find the ages of all lady.

Solution:

Let the age of grandma be 'x'.

Now Given:

The daughter is 44 less than the grandma's age.

So we can say that;

Age of the Daughter = $x-44$

The great-grandma is 22 more than the grandma's age.

So we can say that;

Age of the great grandma  = $x+22$

The mother is 80 less than twice the grandma's age.

So we can say that;

Age of the mother  = $2x-80$

Now we can say that;

Total years they all lived  is equal to sum of age of grandma, Age of the Daughter, Age of the great grandma, Age of the mother.

framing in equation form we get;

$x+x-44+x+22+2x-80=193\\\\5x-102=193$

Adding both side by 102 we get;

$5x-102+102=193+102\\\\5x= 295$

Dividing both side by 5 we get;

$\frac{5x}{5}=\frac{295}{5}\\\\x= 59\ years$

Hence Age of Grandma = 59 years.

Age of great Grandma = $x+22 =59+22 = 81\ years$

Ages of Mother = $2x-80= 2\times 59-80 = 38\ years$

Age of Daughter = $x-44=59-44=15\ years$