Help with Math Problem

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ttfanatic

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Jun 20, 2011
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I have a problem that I am trying to solve and was hoping someone could help me with it?

The problem is:
Customers bought 80% of their tubes and 40% of their needles from a company, accounting for $6,000,000 in sales.

(Price of tubes x No. of tubes) + (Price of needles x No. of needles) = $6,000,000

Price of tubes = $0.08
Price of needles = $0.075
For each needle are needed 2.5 tubes

I need to determine the number of tubes sold and the number of needles sold based on total sales of $6 million.

Can anyone help me solve or show me the formula/process that I can use to solve?

Thank you
 
You have not quite gotten the entire problem in hand.

T = # of tubes bought from company
T / 0.80 = Total number of tubes purchased in the entire economy
N = # of needles bought from the company
N / 0.40 = Total number of needles purchased in the entire economy

The fun part is the repationship between needles and tubes. They were not necessarily purchased from the same place!!

(T / 0.80) = (N / 0.40)*2.5 -- The relationship holds only for the entire economy.

You have already 0.08*T + 0.075*N = 6000000
 
Thanks for your input.
Below is the feedback that I had received previously. I cannot follow how the person came up with X = 5Y. Please help explain if this is correct.
Price T = $0.08
Price N = $0.075
X number of tubes sold to the company
Y number of needles sold to the company
0.08X + 0.075Y = 6,000,000
For each needle are needed 2.5 tubes
T number of tubes company sold
N number of needles company sold
So, T/N=2.5 and since 40%N=Y, 80%T=X ? 80%T/40%N=X ? X/Y=5Y
0.08 x 5Y + 0.075Y = 6,000,000
0.4Y + 0.075Y = 6,000,000
Y = 12,600,000 and X = 5Y = 63,000,000
So 63,000,000 tubes and 12,600,000 were sold by the company
 
I do not understand the defintions concerning selling things TO the company. That's not in the problem statement you presented. Ha sthe question been changed?

Are you SURE we're working with ONE problem statement?

Why don't you show YOUR work and you tell me what YOU think?
 
Sorry for the confusion. It was late last night when I replied. It is one problem. The tubes and needles are being purchased from the company not sold to it.

X number of tubes purchased from the company
Y number of needles purchased from the company

T number of tubes
N number of needles

T/N=2.5
and since 40%N=Y
80%T=X ?
80%T/40%N=X/Y ?
X/Y=5Y
0.08 x 5Y+0.075Y = 6,000,000
0.4Y+0.075Y=6,000,000
Y=12,600,000 and X=5Y=63,000,000
So 63,000,000 tubes and 12,600,000 were purchased by the company
 
OFTEN helps if you create your own problem with SIMPLE givens, based on the problem you're given.
Like:
A's are purchased at $5 each.
B's are purchased at $3 each.
2 B's are purchased for each A
Total spent = $66

5A + 3B = 66
Since B = 2A:
5A + 3(2A) = 66
11A = 66
A = 6

Now go back and solve your "complicated sounding problem" the same way; kapish?
 
Denis, thank you very much. I was able to solve my problem very quickly using your simple approach. I really appreciate the help.
 
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