Question

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 1

`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)\\ (2)/(3)-1kg\ \ \ to\ make\ 1kg\ we\ need\ (2)/(3)\ Turkish\ coffee\\ a\ \ \ -300kg\ \ \ to \ make\ 300kg\ we\ need\ a\ Turkish\ coffee\\ 300*(2)/(3)=a\\ a=200kg\ \ He\ need\ 200kg\ Turkish\ coffee.`