SOLUTION: Sam�s age is one-fourth of his father�s age and two-third of his sister Rita�s. What is the ratio of the ages of Sam, Rita and their father respectively?

Question 1102638: Sam�s age is one-fourth of his father�s age and two-third of his sister Rita�s. What is the ratio of the ages of Sam, Rita and their father respectively?

Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Since no ages are given, I will just say that
the father is yrs old ( reasonable ).
Then Sam is
------------------------------
Let = Rita's age
given:

-----------------------
Sam : Rita : father =
12 : 18 : 48 =
2 : 3 : 8

Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Choosing reasonable numbers, as the other tutor did, is a valid way to solve this kind of problem. You can also solve them using the given ratios, without choosing numbers.

Let's use F, S, and R for the ages of the father, Sam, and Rita, respectively. Then the given information tells us

S:F = 1:4
S:R = 2:3

Sam is part of both of these ratios. So now modify these ratios by multiplying one or both of them by constants, so that the numbers for Sam are the same in both ratios. Doubling the first ratio will do that:

S:F = 2:8
S:R = 2:3

Then we can combine them into a single ratio relating all three ages:

S:R:F = 2:3:8
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