Answer to Question #121290 in Statistics and Probability for Harriet

Question

If 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

Let the age of Kissi ,Esinam,Lariba are $x,y,z$ respectively.

Then According to question,

$x:y=3:5 \ , \ y:z=3:5$

And $x+y+z=147$

Since, $x:y=3:5 \implies \frac{x}{y}=\frac{3}{5} \implies x=\frac{3y}{5}$

$y:z=3:5 \implies \frac{y}{z}=\frac{3}{5} \implies z=\frac{5y}{3}$

$\therefore \frac{3y}{5}+y+\frac{5y}{3}=147$

$\implies \frac{9y+15y+25y}{15}=147$

$\implies 49y=147×15$

$\implies y=\frac{147×15}{49}=3×15=45$

$\therefore x=\frac{3×45}{5}=27 \ and \ z=\frac{5×45}{3}=5×15=75$

The age difference between oldest and youngest $=75-27=48$