Question

Ellen is three times as old as Kesha now. In six years, Ellen will be twice as old as Kesha. How old are both girls now?

Answer 1

$\sf\red{\underline{\underline{Answer:}}}$

$\sf{Ages \ of \ Ellen \ and \ Kesha \ are}$

$\sf{18 \ and \ 6 \ years \ respectively.}$

$\sf\orange{Given:}$

$\sf{\implies{Ellen \ is \ three \ times \ as \ old \ as \ Kesha}}$

$\sf{\implies{In \ six \ years, \ Ellen \ will \ be \ twice}}$

$\sf{as \ old \ as \ Kesha.}$

$\sf\pink{To \ find:}$

$\sf{Ages \ of \ Ellen \ and \ Kesha.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{Let \ x \ be \ the \ common \ factor}$

$\sf{According \ to \ the \ first \ condition}$

$\sf{Age \ of \ Ellen=3x}$

$\sf{Age \ of \ Kesha=x}$

$\sf{According \ to \ the \ second \ condition.}$

$\sf{3x+6=2(x+6)}$

$\sf{3x+6=2x+12}$

$\sf{3x-2x=12-6}$

$\boxed{\sf{\therefore{x=6}}}$

$\sf{\therefore{Age \ of \ Kesha=6 \ years}}$

$\sf{Age \ of \ Ellen=3(6)=18 \ years.}$

$\sf\purple{\tt{\therefore{Ages \ of \ Ellen \ and \ Kesha \ are}}}$

$\sf\purple{\tt{18 \ and \ 6 \ years \ respectively.}}$

Answer 2

Given :

• Ellen is three times as old as Kesha now.

• In six years, Ellen will be twice as old as Kesha.

To find :

• Age of both girls now = ?

Step-by-step explanation :

Let, the age of Kesha be x.

Then, the age of Ellen be 3x.

After 6 years Ellen age = 3x + 6.

After 6 years Kesha age = x + 6

According to the question :

➮ 2(x + 6) = 3x + 6

➮ 2x + 12 = 3x + 6

➮ 2x - 3x = 6 - 12

➮ -1x = - 6

➮ x = 6.

Therefore, We get the value of, x = 6 years.

Hence,

The age of Kesha, x = 6 years.

The age of Ellen, 3x = 3 × 6 = 18 years.