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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
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