Let us form the simultaneous equations in each of the following cases and see whether the solution of them is possible or not.The sum of my elder sister’s present age and my father’s present age is...

Question

Let us form the simultaneous equations in each of the following cases and see whether the solution of them is possible or not.
The sum of my elder sister’s present age and my father’s present age is 55 years. By calculating, I observed that after 16 years, my father’s age will be two times of my sister’s age.

(a) Let me draw the graph after framing simultaneous equations.

(b) With the help of graph, let me find out whether the general solution of two equations can be determined.

(c) Let me write the present age of my elder sister and father from the graph.

Philoid · Accepted Answer

Let take my sister’s present age to be = X

My father’s present age as = Y

Given that

The sum of my elder sister’s present age and my father’s present age is 55 years.

So we can write it as

Sister’s age + father’s age =55

X+Y = 55 ………… (1)

Also given that after 16 years, my father’s age will be two times of my sister’s age.

So father’s age after 16 years will be (Y+16)

And sister’s age after 16 years will be (X+16)

So our new equation become

Father’s age = 2× (sister’s age)

Y+16 = 2×(X+16)

Y = 2X +16 ………… (2)

Equation (1)

X +Y=55

Equation (2)

Y = 2X +16

After plotting the lines, we can determine the intersection point of lines.

You can clearly see in the figure given below.

Red line for equation (1)

Blue line for equation (2)

We can satisfy the point (13, 42)

Equation (1)

X+Y=55

13 +42 = 55

AND EQUATION (2)

Y=2X+16

42 =2×13+16

HENCE, sister’s age is =13 years

Father’s age is =24 years