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:

m-d= 24

m= 24+d-----1

1/m+1/d= 1/9

d+m/md= 1/9

9(d+m)= md

put 1 in this equation

9(d + 24 + d) = d(24+d)

9(2d + 24) = d x 24 + d x d

2d x 9 + 24 x 9 = 24d + d^2

18d + 216 = 24d + d^2

0= d^2 +24d - 18d -216

0 = d^2 + 6d -216

0 = d^2 +18d -12d -216

0 = d(d + 18) - 12(d + 18)

0 = (d-12)(d+18)

case 1

d +18 = 0

d= -18

rejected cause age is never negative

case 2

d-12 = 0

d= 12

Thus 12 is the correct value of d

if d is 12

then m = d + 24

= 12+24

= 36

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.