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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?

Respuesta :

Answer:

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  

Step-by-step 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 = [tex]\frac{1}{3}[/tex] of  The age of Lauren's

I.e A = [tex]\frac{1}{3}[/tex] × L

And ,

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

I.e K = 2 × L

∴ [tex]\frac{1}{3}[/tex] × L + L + 2 × L = 80

Or,  [tex]\frac{1}{3}[/tex]  L + 3 L = 80

Or, [tex]\frac{10}{3}[/tex]  L = 80

So, 10 L = 3 × 80

∴   L = [tex]\frac{240}{10}[/tex]

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 = [tex]\frac{1}{3}[/tex] × L

Or, A =  [tex]\frac{1}{3}[/tex] × 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

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