Question

In six years, jill will be twice amanda's age. One year ago, jill was nine times amanda's age. How old is jill now?

Answer 1

let age of jil be x and age of ananda be y
according to 1st condition
x+6=(y+6)2
x-2y =6 1st×9
2nd condition
x-1=(y-1)9
x-9y=-8 2nd ×2
after adding both the equation
x=10

Answer 2

Given:

In six years, Jill will be twice Amanda's age. One year ago, jill was nine times Amanda's age.

To find:

The present age of Jill.

Solution:

The present age of Jill is 10 years.

To answer this question, we should follow the following steps:

Let the present age of Jill and Amanda be x and y years respectively.

After 6 years,

The age of Jill = (x + 6) years.

The age of Amanda = (y + 6) years.

So,

According to the question,

We have,

$x + 6 = 2(y + 6) \: \: \: (i)$

Also,

One year ago,

The age of Jill = (x - 1) years

The age of Amanda = (y - 1) years

So,

$x - 1 = 9(y - 1) \: \: (ii)$

(i) can be written as

$x + 6 = 2y + 12$

$x - 2y = 6 \: \: (iii)$

and

(ii) can be written as

$x - 1 = 9y - 9$

$x - 9y = - 8 \: \: (iv)$

On subtracting (iv) from (iii), we get

$7y = 14$

$y = 2 \: years$

On putting the value of y in (iii), we get

$x - 2(2) = 6$

$x = 10 \: years$

Hence, the present age of Jill is 10 years.