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?

1 Answer
May 16, 2015

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

r = m/3

r = 2.5d = (5/2)d

r+m+d = 66

and we are trying to determine r.

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

Multiplying the second equation by 2/5 on both sides, we find d = (2/5)r

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

66 = r+m+d = r + 3r + (2/5)r

= (1+3+(2/5))r

= (5/5 + 15/5+2/5)r

= ((5+15+2)/5)r

= (22/5)r

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

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.