A coffee shop mixes Brazilian coffee worth $5 per kilogram with Turkish coffee worth $8 per kilogram. The mixture is to sell for $7 per kilogram. How much of the Turkish coffee should be used to make 300 kg of the mixture?

Question

NeomaFodor NeomaFodor

31-07-2014
Mathematics

Answered

A coffee shop mixes Brazilian coffee worth $5 per kilogram with Turkish coffee worth $8 per kilogram. The mixture is to sell for $7 per kilogram. How much of the Turkish coffee should be used to make 300 kg of the mixture?

Answer :

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luana luana · Answer 1 · 2014-07-31T19:04:53-04:00

[tex]Brazilian-5$\ per\ kg\\\\ Turkish-\ 8$\ per\ kg\\\\ x-amount\ of\ Brazilian\ coffee\\ y-amount\ of\ Turkish\ coffee\\\\ x*5+(1-x)*8=7\\ 5x+8-8x=7\\ -3x=-1\\ x=1/3\\ y=2/3\\\\ To\ make\ 300kg\ we\ need:\ (from\ proportion)\\ \frac{2}{3}-1kg\ \ \ to\ make\ 1kg\ we\ need\ \frac{2}{3}\ Turkish\ coffee\\ a\ \ \ -300kg\ \ \ to \ make\ 300kg\ we\ need\ a\ Turkish\ coffee\\ 300*\frac{2}{3}=a\\ a=200kg\ \ He\ need\ 200kg\ Turkish\ coffee.[/tex]