Question

The ratio of the ages of Kissi and Esinam is 3:5 and that of Esinam and Lariba is 3:5 and

the sum of the ages of all 3 is 147 years, what is the age difference between oldest the youngest

Answer 1

The age difference between oldest the youngest is of 48 years.

Explanation:

We can solve this question using a system of equations.

I am going to say that:

Kissi's age is x.

Esinam's age is y.

Lariba's age is z.

The ratio of the ages of Kissi and Esinam is 3:5

This means that
`(x)/(y) = (3)/(5)`, so
`5x = 3y`

That of Esinam and Lariba is 3:5

This means that
`(y)/(z) = (3)/(5)`, so
`5y = 3z`

The sum of the ages of all 3 is 147 years

This means that
`x + y + z = 147`

What is the age difference between oldest the youngest

z is the oldest

x is the youngest.

First i will find y.

We have that, from the equations above:
`x = (3y)/(5)` and
`z = (5y)/(3)`

So

`x + y + z = 147`

`(3y)/(5) + y + (5y)/(3) = 147`

The lesser common multiple between 5 and 3 is 15. So

`(3*3y + 15*y + 5*5y)/(15) = 147`

`49y = 147*15`

`y = (147*15)/(49)`

`y = 45`

Youngest:

`x = (3y)/(5) = (3*45)/(5) = 27`

Oldest:

`z = (5y)/(3) = (5*45)/(3) = 75`

Difference:

75 - 27 = 48

The age difference between oldest the youngest is of 48 years.