Appears Basic and simple, please help find what we are doing wrong or not noticing

[Bernie the Cash]

Okay, I've been stumped by this apparently simple to answer math question that doesn't seem to be working out....for anyone, for an inexplainable reason. If you can explain it, several of us would be very appreciative. To start, this problem aross from the Water Company that I work for. Our desire is to show a benifit in increasing the value of 1EDU = 700GPD to reduce fees for our customers. 1 EDU is defined as; (1 Equivilant Dewelling Unit = 700 Gallons Per Day). We have a development that is going to use 10,386 GPD. The current example of calculating our fees is as follows;

10,386GPD / 700GPD/EDU = 14.84EDU (exmp. "A"). Now, the next step is multiplying the value of EDU by the cost per EDU at $9,667.00. Shown as (14.84EDU x $9,667EDU = $ 143,458.28)

This is the cost of the project pursuant to its actual water usage as compaired back to what a typical home is expected to use per day. If you increase the GPD value of an EDU, then you in effect, reduce the fees owed by the project. Our problem is the we want to increase the 700GPD/EDU value by 50% (exmp. "B") and then double it up to 100% (exmp. "C"). Now that you have the story, please see the challenges below.

Constant number to be divided: 10386 Gallons Per Day (GPD)

"Example A" = 700 GPD (exmp.-10386GPD/700GPD per EDU = 14.84EDU's)
"Example B" = 1050 GPD (exmp.-10386GPD/1050GPD per EDU = 9.89EDU's)
"Example C" = 1400 GPD (exmp.-10386GPD/1400GPD per EDU = 7.42EDU's)

***** Do you see the descrepency? Example "C" is exactly what we expected to see at half the value of Example "A". However, there is a problem when calculating the midway value of Example "B". It doesn't come up to the true midpoint of 11.31 EDU's. (Midpoint between 14.84EDU's and 7.42EDU's = 11.31EDU's) - There are several ways of writing this problem out, but we couldn't explain why it isn't in the middle and you can see when you plug the answers back into the fee calculation above why this matters so much. That and we are growing bald spots trying to figure this out. PLEASE HELP!?!? :'(

 

[tkhunny]

First, you must abandon your incorrect idea of the "true midpoint". You neither know what that means nor have you succeeded in defining it.

Try this.

700 = 1 * 700
1050 = (3/2) * 700
1400 = 2 * 700

Thus

10386 / (1*700) = 14.83714
10386 / ((3/2)*700) = 9.89143
10386 / (2*700) = 7.41857

We see that

7.41857*2 = 14.83714
9.89143*(3/2) = 14.83714

The arithemetic is fine. You were expecting a result half way between 1/2 and 1. That is 3/4. Why would you expect a result at 3/4 when the factor you have used is 2/3?

You will need to rethink what it is you are doing. If you were multiplying by nice numbers, it might work as you expect. Since you dividing by these values, it is not right in your perception.

Where does that leave us?