Question

Ravish tells his daughter Aarushi, "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"..If present ages of Aarushi and Ravish are x and y years respectively, represent this situation algebraically as well as graphically

Answer 1

1. Arushi = 12 years, Rabish = 42 years (Both algebraically and graphically)

Explanation:

1. Algebraic solution

Given,

The age of Arushi is X years

The age of Ravish is Y years

7 years ago the age of Arushi was (X-7)

7 years ago the age of Ravish was (Y-7)

According to the question , (Y-7) = 7(X-7)......(i)

Again according to the question Y+3 = 3(X+3).......(ii)

From equation (i),

Y-7 = 7(X - 7)

or, Y = 7(X - 7)+7

or, Y = 7X - 49 + 7

or, Y = 7X - 42......(iii)

Putting the value of Y in equation (ii)

Y + 3 = 3(X + 3)

or, 7X - 42 + 3 = 3X + 9

or, 7X - 3X = 9 + 42 - 3

or, 4X = 48

or, X = 48/4

or, X = 12

Putting the value of X in equation (iii)

Y = 7X - 42

or, Y = 7*12 - 42

or, Y= 84 - 42

or, Y = 42

2. graphical solution

For equation (i), (Y-7) = 7(X-7)

X Y (X,Y)

5 -7 (5,-7)

6 0 (6,0)

For equation (ii), Y+3 = 3(X+3)

X Y (X,Y)

0 6 (0,6)

-2 0 (-2,0)

The graph is shown as attachment,

If you take the scale on y-axis as 5 or 10, you will see that the two lines intersect at the point (12, 12) .

Hence, the age of Arushi is 12 years, and the age of Ravish is 42 years.