Question

Mrs Tan has 2 daughters, Phoebe and Jody. The highest common factor and lowest common multiple of their ages are 3 and 168 respectively.If Phoebe is 3 years older than her sister, find her age. ​

Answer 1

Phoebe's age = 24 years.

Explanation:

Given:

Highest Common Factor and Lowest Common Multiple of the ages are 3 and 168 respectively.

Phoebe is 3 years older than Jody.

To find:

The age of Phoebe = ?

Solution:

Here, We have two numbers whose

HCF = 3 and

LCM = 168

Let the age of Phoebe = P years and

Let the age of Jody = J years

As per given statement:

`P = J + 3 ...... (1)`

Let us learn about the property of LCM and HCF of two numbers.

The product of LCM and HCF of two numbers is equal to the product of the two numbers themselves.

LCM
`*` HCF = P
`*` J

`\Rightarrow P* J = 3 * 168 \\\Rightarrow P* J = 504`

Putting the value of P from equation (1):

`\Rightarrow (J+3)* J = 504\\\Rightarrow J^2+3J-504 = 0\\\Rightarrow J^2+24J-21J-504 = 0\\\Rightarrow J(J+24) - 21(J+24) = 0\\\Rightarrow (J - 21)(J+24) = 0\\\Rightarrow J = 21, -24`

Negative value for age is not possible So, Jody's age = 21 years

Using equation (1):

Phoebe's age = 21 + 3 = 24 years.