Expert: Josh - 1/11/2006

Question
Hello:

It's been a long time since I had algebra.

Do you know what the following indicates? Find an expression for each in sixths of Sarah's age.

And also, how old is each?  
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Followup To
Question -
Hello:

Here is my question:

Sarah's age is 2/3 of Mary's and 3/4 of Ruth's. The sum of their ages is 46 years. How old is each?

NOTE: Find an expression for each in sixths of Sarah's age.

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The question came from a chapter of an old textbook on arithmetic. The chapter pertains to fractions and makes no mention of algebra calculations. Try to determine the answer without using an algebraic calculation?

I thank you for your assistance.



Answer -
Translating the information into algebraic expressions is probably the best way of tackling this problem.

Let "s" be Sarah's age; "m" be Mary's age; "r" be Ruth's age.

s=(2/3)*m ...[#1a]
s=(3/4)*r ...[#1b]
s+m+r=46. ...[#2]

m=(9/8)*r ...[#5]

Express s and m in terms of "r" in [#2],
(3/4)*r+(9/8)*r+r=46

Solve for "r", then work out the rest:)


Answer
I did not complete the question, because I want to give you the opportunity to work it out yourself. I've given you enough hints I think, to work out the values of "r", "m" and "s".

Re: "Find an expression for each in sixths of Sarah's age" This is weird and confusing. I'm not sure if it amounts to anything useful. Why not just determine the age for Ruth, Mary and Sarah. I presume that you can carry on from [#5].

Please be specific in your follow-up if there's something that you don't follow.