How do I approach this Algebra problem?

JoeyW said:
They're just unit-less numbers that represent how you can partition the given amount of material into concurrent parts of size 0.14 and 0.407.
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Please refer to the original post (#1) and define "x" and "y" in those terms.
 
Benjamin7399 said:
Frank & Frank industries developed colors for knitting wools for special purpose applications. The color baths are mixed using two different ingredients - the color and an agent that makes the color more UV stable. Other ingredients go into the color baths that are not important to the analysis. The mix of the two ingredients depends on the product type. You must calculate the amount of blue color bath you can prepare for Product P and Product Q. You have 390 liters of blue color and 543 liters of UV agent. The following table indicates how much of the blue color (in liters) and how much of the UV agent (in liters) you need to make a liter of color bath for Product P and Product Q.

​

Product PProduct Q
Blue Color (in liters)0.140.407
UV agent (in liters)0.4750.444


Suppose you have to prepare the color baths for Product P and Product Q at the same time. How many liters of color bath for Product P and Product Q can you prepare using the available inventory of the color blue and the UV agent? Round your result to two decimal digit.

Calculate Amount of color bath for Product P:
Calculate Amount of color bath for Product Q:

I've been stuck with this problem for a week now. I'm not sure what the correct answer is. I approached this like a linear equation

0.14x+0.407y=390
0.475x+0.444y=543

Amount of color bath for Product P: 0.14x+0.475x
Amount of color bath for Product Q: 0.407y+0.444y

Am I missing something? Is this the correct way to approach this? If not please teach me. Thanks in advance.
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When you wrote:

0.14x + 0.407y = 390......................................................(1)

0.475x + 0.444y = 543......................................................(2)

What did x & y stand for?

[My apologies - the response #19 was intended for the OP - Benjamin]
 
x and y represent the ratio of the desired amount of color bath to the minimum quantity per unit for products P and Q respectively.
 
JoeyW said:
x and y represent the ratio of the desired amount of color bath to the minimum quantity per unit for products P and Q respectively.
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I'll await response from OP [Benjamin].
 
I'd like to apologize for not being more rigorous with my responses. I'll try to be more mindful in future posts. ?
 
I came across this old thread and I have been given the same maths problem and also am unable to solve it using these techniques. Because x and y per product make up less than a litre but contribute to a finished litre of product, I wonder if this plays into the answer, however I have been unable to get a correct answer with scaling up, either. How mysterious!! Any help much appreciated.
 
travellingsam said:
I came across this old thread and I have been given the same maths problem and also am unable to solve it using these techniques. Because x and y per product make up less than a litre but contribute to a finished litre of product, I wonder if this plays into the answer, however I have been unable to get a correct answer with scaling up, either. How mysterious!! Any help much appreciated.
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This is a very confusing thread because of the noxious intervention by joey, who i hope has been banned, and because it involved a computer-based learning system, which are notorious for being frequently wrong. It started with a problem that specifically noted that additional ingredients were needed in each liter of bath and that asked for an approximate answer. As far as I can see it was never clarified if the OP scaled up at all, let alone how and when he rounded.

Please show us the work you did and what makes you believe it to be wrong.
 
JoeyW said:
@Otis, I'm sorry for not being clearer, and thank you for pointing out the round-off error. The quantity for P is approximately [math] 390 - 0.14 \bigg \lfloor \frac{390}{0.547} \bigg \rfloor [/math], while Q is [math] 390 - 0.407 \bigg \lfloor \frac{390}{0.547} \bigg \rfloor [/math]. It isn't necessary to round down [math] \frac{390}{0.547} [/math], it's just a bad habit I've fallen into. ?
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can you please tell me how did you get 0.547 ?
 
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