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A trader buys $15$ Kg of Arabian coffee powder at $x$ dollars per kg and $25$ kg of Brazilian coffee at $y$ dollars per kg. He mixes the two types of coffee powder in a ratio $3 : 5$ and packs the mixture into packets each of which contains $100$ grams of the mixture. He sells the packs for $ 40x + 48 y / 640 $ dollars. Find an expression for the selling price of all the packets of coffee powder in terms of $x$ and $y$.

I clearly knows that I need to find the cost price of the coffee powder .

I done up a ratio of the price of the coffee powder = $ 3x : 5y $ Why is the cost price of the coffee powder not $ 3x + 5y $ ?

Can I get a hint on how to carry on? Thanks in advance !

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  • $\begingroup$ Do you mean $\frac{40x+48y}{640}?$ $\endgroup$ – Bobson Dugnutt Sep 13 '16 at 12:52
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Hint: The seller can make $\frac{15+25}{0.1}=400$ packages. You know the selling price of each package. This allows you to compute the total selling price.

If you want to find the total profit, use that you also know that it cost the seller $15x+25y$ to be able to make these packages. Then simply subtract the two.

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  • $\begingroup$ I'm struggling to understand why does it cost the seller $15x+25y$ instead of $3x + 5y $ $\endgroup$ – user307640 Sep 13 '16 at 13:04
  • $\begingroup$ @user307640 Because s/he bought $15$ kilos and $25$ kilos... $x$ and $y$ are the prices per kilo. $\endgroup$ – Bobson Dugnutt Sep 13 '16 at 13:05
  • $\begingroup$ I suspect it's a language problem for me .. Just to check .. When he mixes the two types of coffee powder in a ratio of 3:5 , Do we assume that he mixes all the 15 kg of Arabian coffee powder and 25 kg Brazilian coffee ? $\endgroup$ – user307640 Sep 13 '16 at 16:41
  • $\begingroup$ @user307640 Well, we might as well, because that would produce a ratio of 3:5 (notice that $15/25=3/5$) :) Also notice that the questions ask for "find an expression for the selling price of all the packets of coffee powder", i.e., the 40 kilos. $\endgroup$ – Bobson Dugnutt Sep 13 '16 at 17:42
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"I done up a ratio of the price of the coffee powder = 3x:5y. Why is the cost price of the coffee powder not 3x+5y? "

It is. What makes you think it isn't? Of course, that is not what the question asked so would not be the "answer" to the question. The question asked for the selling price.

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  • $\begingroup$ Perhaps I don't know the true meaning of "cost price", but surely you agree that the seller spent $15x+25y$ dollars on the entire batch, right? So what does the figure $3x+5y$ represent? $\endgroup$ – Bobson Dugnutt Sep 13 '16 at 14:14
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It cost the dealer 15x+ 25y dollars for the entire 15+ 25= 40 kg of coffee. That is an average price of (15x+ 25y)/40= 5(3x+ 5y)/40= (3x+ 5y)/8 dollars per kilogram.

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