Expert: Scott A Wilson - 10/29/2009

Question
Hello:

2/3 of Mary’s age equals Sarah’s age and 3/4 of Ruth’s age equals Sarah’s age. If the total ages equal 46, how old is each girl?

Answer: Mary 18, Ruth 16, Sarah 12

Solution:

3/2 of Sarah’s age equals Mary’s age.
4/3 of Sarah’s age equals Ruth’s age.
6/6 of Sarah’s age equals Sarah’s age.

46 divided by 23/6 equals Sarah’s age of 12.

Can the following similar situation be solved if the two girls ages do not equal Sarah’s age?

2/3 of Mary’s age equals Ruth’s age and 3/4 of Ruth’s age equals Sarah’s age. How old is each girl?

There ages will not be the same as those in the above example.

I thank you for your reply.


Answer
2M/3 = R, 3R/4 = S, so putting R in gives 3(2M/3)/4 = S, so M/2 = S, so M = 2S.
Also, it can be seen that R = 4S/3.

The sum of that ages is still 46.

Since this time we have M+R+S=46, we can put in what M and R are.

This says 2S + 4S/3 + S = 46, so 6S/3 + 4S/3 + 3S/3 = 46.
this gives 13S/3 = 46, or S = 3*46/13, or S = 138/13 = 10 8/13.

R is (4/3)S = (4/3)(138/13) = 184/13 = 14 2/13.

M is 2S = 2(138/13) = 276/13 = 21 3/13.

M+R+S=(276+184+138)/13 = 598/13 = 46.

It can be done, but I've never heard anyone say,
"Yeah, my kids are 10 8/13, 14 2/13, and 21 3/13 years old."

Generally, age is f(x) = trunc(n) where n is the age and
trunc(n) is the highest integer that is n or below.