Expert: Scott A Wilson - 10/17/2009

Question
QUESTION: Hello:

5% X $2000 = $100

2% X $1000 = $20

Can any of the fractions of 1/6 or 5/6 be determined from the above calculation if the amounts of $2000 and $1000 were missing?

5% X $? = $100

2% X $? = $20

I believe the average is $120 or 4%. Is there a somewhat simple method to find any of these fractions 1/6 or 5/6 by using $120 and or 4% or any of the information from the incomplete calculation?


I thank you for your reply.

ANSWER: I'm not sure what is mean by the question about 1/6 or 5/6.
If the values were missing, you would have 5% * X = $100 and 2% * X = $20.

5% is the same as /20, so X/20 = $100 => X = $2,000.
2% is the same as /50, so X/50 = $20 => X = $1,000.

The average return is ($2,000 + $1,000)/2 = $1,500.
The average interest, ignoring how much money is involved, is (2% + 5%)/2 = 3.5%.

The overall average interest is, yes, $120.  The overall money involved is, yes, $3,000.
120/3000 = 4/100 = 4%, and that is right as well.

Again, where do 1/6 or 5/6 come into play?


---------- FOLLOW-UP ----------

QUESTION: Hello:

I want to thank you for your reply.

If I can determine 1/6 and or 5/6, I can determine the amounts of $2000.00 and $1000.00. 1/6 of $120.00 equals $20.00 and 5/6 of $120.00 equals $100.00. The fractions come from 20/120 equals 1/6 and 100/120 equals 5/6. But I do not know how to divide 120 into $20.00 and $100.00.

I hope this information helps.

ANSWER: I see it now.  That is, 20/120 = 1/6 = 16 2/3% and 100/120 = 5/6 = 83 1/3%.

I would divide it by 1 $20 and 5 $20's.
Maybe I would divide it by 1 $20 and 2 $50's.

That's probably not what you meant, but if you take $120 - $20,
you get $100 left for the other person.

The $100 came as 5% of $2000 and the $20 cam as 2%  of $1000.

I've told you a few possibilities of what bills they could be,
the fact that 120 minus one is the other, and
where the percentages and the money initiated them.

Is this what was being looked for?


---------- FOLLOW-UP ----------

QUESTION: Hello:

I want to thank you for your follow-up reply.

What I need to know is how I can determine how to divide the $120.00 so that I get $20.00 and $100.00? The amounts of $2000.00 and $1000.00 are not known. I thought that there may be some simple calculation available.

I thank you for your help and assistance.

Answer
Well, $100.00 + $20.00 = $120.00.

If we look at $20/$120, we can cancel the $ and get 20/120.
A 0 can also be dropped in both the numerator and denominator give 2/12.
Divide top and bottom by 2 and get 1/6.

If we look at $100/$120, we can cancel the $ and get 100/120.
A 0 can be dropped in both the numerator and the denominator, giving  10/12.
The numerator and denominator can be divided by 2, giving 5/6.

Doing this, we don't even have to know about the $1,000 or $2,000.

That is where the 1/6 and 5/6 come from.