PROBLEM NO 3:: x/2-y/3 =4, 2x/3-y/4 =1
Answers
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.
Ans. Let the present age of Aftab = x And, present age of his daughter is represented as = y Seven years ago, Aftab’s age = x – 7 Age of Aftab’s daughter = y – 7 According to the question, (x – 7) = 7 (y – 7 ) x – 7 = 7 y – 49 x – 7y = – 49 + 7 x – 7y = – 42 … (i) x = 7y – 42 Putting y = 5, 6 and 7, we get x = 7 × 5 – 42 = 35 – 42 = – 7 x = 7 × 6 – 42 = 42 – 42 = 0 x = 7 × 7 – 42 = 49 – 42 = 7
Three years from now, Aftab’s age = x + 3 Age of Aftab’s daughter = y + 3 According to the question, (x + 3) = 3 (y + 3) x + 3 = 3y + 9 x – 3y = 9 – 3 x – 3y = 6 … (ii) x = 3y + 6 Putting, y = – 2, –1 and 0, we get x = 3 × – 2 + 6 = – 6 + 6 =0 x = 3 × – 1 + 6 = – 3 + 6 = 3 x = 3 × 0 + 6 = 0 + 6 = 6
Algebraic representation From equation (i) and (ii) x – 7y = – 42 … (i) x – 3y = 6 … (ii) Graphical representation