Question

four times the age of a mother is equal to nine times the age of her daughter. after nine years the mother's age will be twice her daughter's age. what is the present age of the daughter?

Answer 1

Step-by-step explanation:

let present age of daughter= x

mother's age be. m

now 4m= 9x

m= 9x/4

after 9 years

daughters age= x+9

mother's age= 9x/4+9= 2(x+9). given

9x/4+9= 2x+18

9x+36/4= 2x+18

9x+36= 4(2x+18)

9x+36= 8x+ 72

9x-8x= 72-36

x= 36 years daughters present age

Answer 2

Given,

4 times the mother's age = 9 times her daughter's age.

After 9 years, the mother's age is twice her daughter's age.

To find,

The present age of the daughter.

Solution,

We can find the solution to this problem simply by following the below steps.

Firstly, suppose that the mother's present age is x years and the daughter's present age is y years.

Now, at present, according to the condition given in the question,

$4x = 9y$.

After 9 years,

Mother's age = $x+9$ years, and

Daughter's age = $y+9$ years.

According to the second condition,

$x+9=2(y+9)$

Simplifying,

$x+9=2y+18\\x-2y=9$

Now, from the previous condition,

$x=\frac{9}{4} y$

Substituting in the equation obtained from the second condition above,

$\frac{9}{4} y-2y=9$

Simplifying,

$\frac{9y-8y}{4} =9$

$9y-8y=36$

$y=36$ years.

Since we supposed y to be the daughter's present age.

Therefore, the present age of the daughter is 36 years.