Question

the difference between the age of a mother and her daughter is 24 years the sum of the reciprocal of their age is 1 by 9 complete the following activity to find mother age​

Answer 1

Answer:

Let the daughter's age be x years. Since age can only be positive, so x=3. Thus mother's age is 21+3=24 years.

Step-by-step explanation:

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Answer 2

Given that

Difference between age of mother and her daughter is 24 year

Sum of reciprocal of their age is

$\frac{1}{9}$

To find

Mother age

Solution

Let

x and y is the age of mother and her daughter then as per given condition

$x - y = 24$

Then as per second given condition

$\frac{1}{x} + \frac{1}{y} = \frac{1}{9}$

By doing cross multiplication we get

$\frac{y + x}{xy} = \frac{1}{9}$

By swaping left hand side and right hand side we get

$9(y + x) = xy$

From first given condition we can take

$x = 24 + y$

then we get

$9(y + 24 + y) = (24 + y)y$

by multiplication we get

${y}^{2} + 6y - 216 = 0$

By factors of this equation we get

$y = - 18 \\ y = 12$

We can not take negative value as age hence

$y = 12$

Hence

Age of daughter is 12year

and age of her mother is

$x = 24 + 12 \\ = 36year$

hence Age of mother is 36year.