Expert: Josh - 12/7/2005

Question
Hello:

How can the unknown amounts be determined for the following calculation?

(What fractional part of 1) X 0.05) + (What fractional part of 1) X 0.02) = 0.04?

Note that the fractions must equal 1.

Answers: 2/3 and 1/3,  2/3 + 1/3 = 1

Check: (2/3 X 0.05) + (1/3 X 0.02) = 0.10/3 +  0.02/3 = 0.12/3 = 0.04

If possible, use a simple calculation for determining the missing fractional amounts

I thank you for your reply.

Answer
Hello,

I don't think it matters whether we are dealing with fractions or not. We can let "x" and "y" be the two unknown quantities. They have to satisfy the constraint that they add up to one.

So, we have x+y=1. Rearranging this, we get y=1-x.
So, the original problem:
"Find x and y, such that 0.05*x + 0.02*y = 0.04"
may be rewritten as
"Find x, such that 0.05*x + 0.02*(1-x) = 0.04".

Expanding the LHS:
0.05*x+0.02-0.02x=0.04
0.03*x=0.02
=> x=2/3, y=1-x.

Regards.