SOLUTION: Three varieties of coffee-Coffee A, Coffee B, and Coffee C-are combined and roasted, yielding a 55-lb batch of coffee beans. Twice as man pounds of Coffee C, which retails for $10.
Question 683962: Three varieties of coffee-Coffee A, Coffee B, and Coffee C-are combined and roasted, yielding a 55-lb batch of coffee beans. Twice as man pounds of Coffee C, which retails for $10.19 per lb, are needed as Coffee A, which sells for $15.21 per lb. Coffee B retails for $12.99 per lb. How many pounds of each coffee should be used in a blend that sells for $12.61 per lb Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website! Let = pounds of coffee A needed
Let = pounds of coffee B needed
Let = pounds of coffee C needed
given:
(1)
(2)
(3)
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Multiply both sides of (3) by
(3)
(3)
Multiply both sides of (2) by and
subtract (2) from (3)
(3)
(2)
Plug this into (2)
(2)
(2)
(2)
(2)
(2)
(2)
and, since
(1)
(1)
(1)
and
(2)
(2)
(2)
(2)
(2)
6.1837 pounds of coffee A are needed
36.449 pounds of coffee B are needed
12.3673 pounds of coffee C are needed
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check:
(2)
(2)
(2)
and
(3)
(3)
(3)
(3)
close enough
