# Thread: Need help with real life math problem

1. ## Need help with real life math problem

Need help with a math problem at work. Not sure if I'm posting in the correct area as its been longer than I'd like to admit since I was in college.

This problem deals with agriculture; specifically low cost methods in bulk fertilizer blending for farmers.

I'm trying to find an equation that fits the following problem:

Two constants 21 & 46
What combination of 24.47% will get you equal to or closest to 5.337.

So for example:

21 x 24.00% = 5.04
46 x 0.47% = 0.21
.......24.47%.. 5.25

The goal is to find an equation that will find the combination of percentages, who's sum is equal to 24.47%, that will get you equal to or closest to 5.337.

I'm probably not wording it correctly, but its driving me nuts. Any help would be much appreciated.

Thx,
C

2. It's not perfectly clear what it is you are doing. I make no promises that the solution to the problem, as it has been presented, will make crops grow any better, but it is likely it can be solved for directly and exactly.

The difficulty is dividing up the 24.47%. Break out your best algebra an initially jut play like you know the answer.

"A" = the piece of 24.47% applied to 21.
0.2447 - A = the piece of 24.47% applied o 46.
Do you see how that identification works? 24.47% is the same as 0.2447, right?

Now, we can use your calculation: 21*A + 46*(0.2447 - A) = 5.337 to represent the EXACT solution to the partitioning.

Time for algebra, again... Can you solve for A?

Note: If you get something like A = 0.2800 or A = -.1500, then something is serious wrong. Can you see why? This is your quiz for the day.

3. Originally Posted by cgardner1
I'm trying to find an equation that fits the following problem:

Two constants 21 & 46
What combination of 24.47% will get you equal to or closest to 5.337.

So for example:

21 x 24.00% = 5.04
46 x 0.47% = 0.21
.......24.47%.. 5.25
Does this represent what you're after as exact result:
(now, * is the multiplication symbol!)

21 * 23.6768% = 4.9724
46 * 00.7932% = 0.3648
.......24.4700%.. 5.3372

If so, then these are the steps:

k = percentage applicable to "21"

21k + 46(.2447 - k) = 5.337
21k + 11.2562 - 46k = 5.337
46k - 25k = 11.2562 - 5.337
21k = 5.9192
k = 5.9192 / 21 = .236768 = 23.6768%

4. Originally Posted by cgardner1
This problem deals with agriculture; specifically low cost methods in bulk fertilizer blending for farmers. I'm trying to find an equation that fits the following problem:

Two constants 21 & 46
For what do these constants stand? How do they relate to mixing fertilizer? What are their units? (kilograms? pounds? per/hectare? moles? something else?)

Originally Posted by cgardner1
What combination of 24.47%...
"A combination" is necessarily comprised of at least two inputs. You've provided a percentage of one input (I think?). How does this percentage relate to the inputs? How many imputs are there?

Originally Posted by cgardner1
...will get you equal to or closest to 5.337.
"Will get you equal or closest to", in what sense? What is the error range, and what are its units? Also, is "5.337" an absolute number, or another percentage? Either way, how much of which input is this, or is this related instead to the output?

Originally Posted by cgardner1
So for example:

21 x 24.00% = 5.04
46 x 0.47% = 0.21
.......24.47%.. 5.25
Yeah.... I don't understand this either. Sorry!

5. Originally Posted by cgardner1
I'm trying to find an equation that fits the following problem:

Two constants 21 & 46
What combination of 24.47% will get you equal to or closest to 5.337.

The goal is to find an equation that will find the combination of percentages, who's sum is equal to 24.47%, that will get you equal to or closest to 5.337.
You have two equations:
21x + 46y = 5.337
x + y = 0.2447

The technique is to re-arrange one of them like so:
x+y = 0.2447
x = 0.2447 - y ; subtracting y from both sides

Now we have something we can stuff into the other equation as a replacement for x:
21x + 46y = 5.337
21(0.2447 - y) + 46y = 5.337

Then solve for y.

6. Take a case "easier" to "follow":

060 30% 18.00
045 15% 06.75
------------------
*** 45% 24.75

Aim: 24.75 changes to 30.00

060 65% 39.00
045-20% -9.00
------------------
*** 45% 30.00

As per previous post by BeeCuz:
Rate on "060" = x
Rate on "045" = .45 - x

60x + 45(.45 - x) = 30
Solve to get x = .65 (or 65%)
So "045" is at .45 - .65 = -.20 (or -20%)

Be aware that most cases will result with "045" getting negative rate.

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