Set up an equation for the following case and also find the solution of the equation:

Mother mother's age is 8 years more than twice her daughter's age. The sum of mother's of age and daughter's age is 56 years.

Given: Mother's age is 8 years more than twice her daughter's age.

To find: We have to find the ages of mother and daughter.

Solution: 

Let the daughter's age = x

Let the mother's age = y

Now,

y = 2x $+$ 8    ...(i)

Also,

x $+$ y = 56

Putting value of y from eq (i)

$x\ +\ ( 2x\ +\ 8) \ =\ 56$

$3x\ +\ 8\ =\ 56$

$3x\ =\ 56\ -\ 8$

$3x\ =\ 48$

$x\ =\ \frac{48}{3}$

$x\ =\ \mathbf{16}$

Putting value of x in eq (i):

$y\ =\ 2( 16) \ +\ 8$

$y\ =\ 32\ +\ 8$

$y\ =\ \mathbf{40}$

Therefore,

Daughter's age = x = 16 years

Mother's age = y = 40 years