Question

At a family reunion, Lauren met up with 2 of her cousins; Kali and Allison. She realized that there were 3 generations of cousins represented with their ages totaling 80 years. If Allison is 1/3 of Lauren's age and Kali is twice as old as Lauren, what are the girl's ages?

Answer 1

The age of three girls as

The age of Allison's is 8 years

The age of Kali is 48 years

The age of Lauren's is 24 years

Explanation:

Let The age of Allison's = A years

The age of Lauren's = L years

The age of Kali's = K years

Now, According to question

The sum of total ages of the three girl's = 80 years

I.e A + L + K = 80 years

And ,

The age of Allison's =
`(1)/(3)` of The age of Lauren's

I.e A =
`(1)/(3)` × L

And ,

The age of Kali's = 2 times The age of Lauren's

I.e K = 2 × L

∴
`(1)/(3)` × L + L + 2 × L = 80

Or,
`(1)/(3)` L + 3 L = 80

Or,
`(10)/(3)` L = 80

So, 10 L = 3 × 80

∴ L =
`(240)/(10)`

I.e L = 24

The age of Lauren's = 24 years

Again ,

K = 2 × L

Or, k = 2 × 24

∴ k = 48

The age of Kali = 48 years

Similarly

A =
`(1)/(3)` × L

Or, A =
`(1)/(3)` × 24

∴ A = 8 years

The age of Allison's = 8 years

Hence The age of three girls as

The age of Allison's is 8 years

The age of Kali is 48 years

The age of Lauren's is 24 years Answer