SOLUTION: Jacki wants to make a micture of nuts to sell in her store consisting of hazelnut and cashews hazelnuts cost 6.50 per pound and cashews cost 4.50 per pound if jackie wants 60 pound

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Question 754396: Jacki wants to make a micture of nuts to sell in her store consisting of hazelnut and cashews hazelnuts cost 6.50 per pound and cashews cost 4.50 per pound if jackie wants 60 pounds total of mixture and the cost to be 5.10 per pound how many pounds of each will she need
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +h+ = pounds of hazelnuts needed
Let +c+ = pounds of cashews needed
+6.5h+ = cost of hazlenuts
+4.5c+ = cost of cashews
+5.1%2A60+=+306+ = cost of mixture
--------------------------------
(1) +h+%2B+c+=+60+
(2) +6.5h+%2B+4.5c+=+306+
-----------------------
(2) +65h+%2B+45c+=+3060+
(2) +13h+%2B+9c+=+612+
Multiply both sides of (1) by +9+
and subtract (1) from (2)
(2) +13h+%2B+9c+=+612+
(1) +-9h+-+9c+=+-540+
+4h+=+72+
+h+=+18+
and, since
(1) +h+%2B+c+=+60+
(1) +c+=+60+-+18+
(1) +c+=+42+
18 pounds of hazelnuts are needed
42 pounds of cashews are needed
check:
(2) +6.5h+%2B+4.5c+=+306+
(2) +6.5%2A18+%2B+4.5%2A42+=+306+
(2) +117+%2B+189+=+306+
(2) +306+=+306+