SOLUTION: Three varieties of coffee - coffee A, Coffee B, and Coffee C - are combined and roasted, yielding a 53-lb batch of coffee beans. Twice as many pounds of Coffee C, which retails for

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Three varieties of coffee - coffee A, Coffee B, and Coffee C - are combined and roasted, yielding a 53-lb batch of coffee beans. Twice as many pounds of Coffee C, which retails for      Log On


   

Question 1179962: Three varieties of coffee - coffee A, Coffee B, and Coffee C - are combined and roasted, yielding a 53-lb batch of coffee beans. Twice as many pounds of Coffee C, which retails for $9.95 per lb, are needed as Coffee A, which sells for $14.99 per lb. Coffee B retails for $12.45 per lb. How many pounds of each coffee should be used in a blend that sells for $11.91 per lb?
Answer by josgarithmetic(39620) About Me  (Show Source):
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COFFEE          PRICE       QTY        COST
A                14.99       a         14.99a
B                12.45       b         12.45b
C                 9.95      2a        9.95*2a=19.9a
MIX             11.91        53

system%2814.99a%2B19.90a%2B12.45b=11.91%2A53%2C3a%2Bb=53%29

Simplify E1. Use E2, substitute for b in E1 and solve for a.
Use a to evaluate the other two coffees quantities.