EXERCISE 3.1
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.
Answers
Answer:
Step-by-step explanation:
Solving such problems involve a good understanding of linear equations.
The key step is to start by assuming variables for ages.
Let the age of Aftab be x years; and the age of his daughter be y years.
"Seven years ago, I was seven times as old as you were then"
Seven years ago, age of Aftab is (x - 7) years; and the age of his daughter is (y - 7) years.
(x - 7) = (y - 7) x 7
=> x - 7 = 7y - 49
=> 7y - x = 42 ....(1)
"three years from now. I shall be three times as old as you will be"
Three years from now, age of Aftab will be (x + 3) years; and the age of his daughter will be (y + 3) years.
(x + 3) = 3 * (y + 3)
=> x + 3 = 3y + 9
=> x - 3y = 6 ....(2)
Adding equations (1) and (2),
(7y - x) + (x - 3y) = 42 + 6 = 48
4y = 48
y = 12
x = 6 + 3y [From equation (2)]
x = 6 + 3 * 12 = 42.
Therefore, their ages are 42 years and 12 years respectively.