Represent the situation algebraically and graphically

Video Explanation

Watch the video explanation below:

Given

Aftab tells his daughter:

• Seven years ago, I was seven times as old as you were.
• Three years from now, I shall be three times as old as you will be.

To Represent

• The situation algebraically
• The situation graphically

Algebraic Representation

Let the present age of Aftab = x years

Let the present age of his daughter = y years

Condition 1: Seven years ago

Aftab’s age = x − 7

Daughter’s age = y − 7

According to the statement:

x − 7 = 7(y − 7)

x − 7 = 7y − 49

x − 7y = −42   …(1)

Condition 2: Three years from now

Aftab’s age = x + 3

Daughter’s age = y + 3

According to the statement:

x + 3 = 3(y + 3)

x + 3 = 3y + 9

x − 3y = 6   …(2)

Graphical Representation

The two linear equations obtained are:

x − 7y = −42   …(1)

x − 3y = 6   …(2)

Table for Equation (1): x − 7y = −42

Take y = 6, then x = 0

Take y = 5, then x = −7

Points: (0, 6) and (−7, 5)

Table for Equation (2): x − 3y = 6

Take y = 0, then x = 6

Take y = 2, then x = 12

Points: (6, 0) and (12, 2)

Steps to Draw the Graph

• Draw a graph of x − 7y = −42 using points (0, 6) and (−7, 5).
• Draw a graph of x − 3y = 6 using points (6, 0) and (12, 2).
• The point of intersection of the two lines gives the solution.

The two lines intersect at the point (42, 12).

Final Answer

Present age of Aftab = 42 years

Present age of his daughter = 12 years

Conclusion

Thus, the given situation is correctly represented both algebraically and graphically, and Aftab’s present age is 42 years while his daughter’s present age is 12 years.