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?

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Answer 1 · 2015-05-16T18:58:22

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

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

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

$r + m + d = 66$ $r+m+d = 66$

and we are trying to determine $r$ $r$ .

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

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

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

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

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

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

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

$= (\frac{22}{5}) r$ $= (22/5)r$

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

$r = 66 \times (\frac{5}{22}) = \frac{66 \times 5}{22} = \frac{22 \times 3 \times 5}{22} = 15$ $r = 66xx(5/22) = (66xx5)/22 = (22xx3xx5)/22 = 15$

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