Expert: Ahmed Salami - 3/10/2006

Question
Hello:

What simple solution, one not requiring algebra if possible, can be used to determine the missing amounts for the following calculation?

(1/2 X ___) + (1/4 X ___) / 20 = 5/20

The answers are 6 and 8.

I have noticed that (1/2 X ___) / 20 represents 3/5 of the answer, 3/5 X 5/20 = 3/20 and that (1/4 X ___) / 20 represents 2/5 of the answer, 2/5 X 5/20 = 2/20.

(1/2 X 6) / 20 = 3/20 + (1/4 X 8) / 20 = 2/20 = 5/20

These calculations indicate that there is a ratio of 3 to 2 between them.  How can I determine these ratios without first knowing what the answers, 6 and 8, are for the above calculation?
If I can determine what these ratios are, I can then determine the missing amounts of 6 and 8.

I thank you for your reply.  

Answer
Hi,
I'm not quite sure how true what you noticed was. Anyway, i can say that there is no specific ratio for this kind of problem in the absence of further information.
Let's take the two numbers to be A and B, then we have
[(1/2)A + (1/4)B]/20 = 5/20
(1/2)A + (1/4)B = 5
multiplying through by 4
2A + B = 20
With this, we can have an infinite amount of A and B
satisfying the relationship.
Examples are A = 0, B = 20
A = 5, B = 10
and so on.
I hope i have helped. You can always get back to me.
Regards.