Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be”. Isn’t this interesting? Represent this situation algebraically and graphically. WITH CORRECT EXPLANATION AND CORRECT GRAPH
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Answer:
Solution:
Assume the present age of Aftab be x years and his daughter be y years.
Present age of Aftab = x years and his daughter = y years
Therefore, 7 years ago, age of Aftab = (x - 7) years and his daughter = (y - 7) years
Using this information and applying the known condition that 7 years ago, Aftab was 7 times as old as his daughter then:
x - 7 = 7(y - 7)
x - 7 = 7y - 49
x - 7y - 7 + 49 = 0
x - 7y + 42 = 0
After 3 years from now, age of Aftab = (x + 3) years and his daughter's age = (y + 3) years
Also, Aftab will be 3 times as old as his daughter which can be represented as:
x + 3 = 3 (y + 3)
x + 3 = 3y + 9
x - 3y + 3 - 9 = 0
x - 3y - 6 = 0
Thus we have,
x - 7y + 42 = 0 ----(1)
x - 3y - 6 = 0 ----(2)
Therefore, the algebraic representation is for equation (1) is:
x - 7y + 42 = 0
-7y = - x - 42
7y = x + 42
y = (x + 42)/7
And, algebraic representation for equation (2) is:
x - 3y - 6 = 0
- 3y = - x + 6
3y = x - 6
y = (x - 6)/3
Let us represent these equations graphically. For this, we need at least two solutions for each equation. Let's tabulate the solutions.
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