Question

At present the sum of Monica's age and her daughter’s age is 44 years. After 2 years, Monica's age will be three times that of her daughter’s age. Find their present ages.

Answer 1

Hint: We have been given with the sum of the ages of monica and her daughter. To solve this we will have to make certain assumptions. Since we have to calculate the present age for both of them.
Therefore,
Let the present age of monica be= years
Let the present age of monica’s daughter be= years
Form the equations based on given information and solve them to find x and y.


Complete step-by-step answer:
Now according to the given condition in the above question ,
Sum of their ages = 44 years
From above discussion we can conclude that
(x+y=44)
now after 2 years the ages that we assumed will be altered by,
age of monica will be years = (x+2) years
age of monica’s daughter will be = (y+2) years
according to the given conditions we will be equating ages of both of them as,
 $
\Rightarrow x + 2 = 3(y + 2) \\
\Rightarrow x + 2 = 3y + 6 \\
\Rightarrow x = 3y + 6 - 2 \\
\Rightarrow x = 3y + 4 \;
 $
Let us put the calculated value of $ x $ in the equation \[x + y = 44\]. We get,
 $
\Rightarrow x + y = 44 \\
\Rightarrow 3y + 4 + y = 44 \\
\Rightarrow 4y + 4 = 44 \;
 $
Taking 4 common from throughout the equation and cancelling from both the sides
 $
\Rightarrow y + 1 = 11 \\
\Rightarrow y = 11 - 1 = 10 \\
\Rightarrow y = 10\, years \
 $
Therefore, age of daughter is = 10 years
And accordingly age of monica is
 $
\Rightarrow x + 10 = 44 \\
\Rightarrow x = 44 - 10 \\
\Rightarrow x = 34\, years \
 $
Therefore the age of Monica is 34 years and the age of her daughter is 10 years.

Note: The above question involves the concept of linear equation in two variables and we know that though every linear equation in one variable has a unique solution but we cannot say about the solution of linear equation involving two variables. In this equation there are two variables. A solution contains one value for x and another value for y which satisfy the given equation.