# My cousin, Ravi, is three times younger than me, but two and a half times older than my daughter. If our total ages are 66, how old is my cousin?

May 16, 2015

Writing $r$ for Ravi's age, $m$ for "my" age and $d$ for "my daughter's" age, we are given:

$r = \frac{m}{3}$

$r = 2.5 d = \left(\frac{5}{2}\right) d$

$r + m + d = 66$

and we are trying to determine $r$.

Multiplying the first equation by $3$ on both sides, we find $m = 3 r$.

Multiplying the second equation by $\frac{2}{5}$ on both sides, we find $d = \left(\frac{2}{5}\right) r$

Substituting for $m$ and $d$ in the third equation, we find

$66 = r + m + d = r + 3 r + \left(\frac{2}{5}\right) r$

$= \left(1 + 3 + \left(\frac{2}{5}\right)\right) r$

$= \left(\frac{5}{5} + \frac{15}{5} + \frac{2}{5}\right) r$

$= \left(\frac{5 + 15 + 2}{5}\right) r$

$= \left(\frac{22}{5}\right) r$

Multiplying both ends of this equation by (5/22) we get:

$r = 66 \times \left(\frac{5}{22}\right) = \frac{66 \times 5}{22} = \frac{22 \times 3 \times 5}{22} = 15$

So Ravi is 15 years old. "my" age is 45 and "my daughter's" age is 6.