SOLUTION: Three varieties of coffee long dash Coffee​ A, Coffee​ B, and Coffee C long dash are combined and​ roasted, yielding a 51​-lb batch of coffee beans. Twice as many pounds of

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Question 1154244: Three varieties of coffee long dash Coffee​ A, Coffee​ B, and Coffee C long dash are combined and​ roasted, yielding a 51​-lb batch of coffee beans. Twice as many pounds of Coffee​ C, which retails for ​$10.39 per​ lb, are needed as Coffee​ A, which sells for ​$14.99 per lb. Coffee B retails for ​$13.99 per lb. How many pounds of each coffee should be used in a blend that sells for ​$12.61 per​ lb?
Should be used
nothing lb. of Coffee​ A,
nothing lb. of Coffee B and
nothing lb. of Coffee C. ​
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This example looks like another similar or identical one solved about a week ago. 
COFFEE        PRICE       QUANTITY        COST

  A           14.99        a             14.99a

  B           13.99        b             13.99b

  C           10.39       2a            2*10.39a

TOTALS                    51 
Avg.          12.61

Form two equations in the unknowns a and b:
system%283a%2Bb=51%2C14.99a%2B2%2A10.39a%2B13.99b=12.61%2A51%29
Simplify and solve the system.

system%283a%2Bb=51%2C35.77a%2B13.99b=643.11%29 simplified system.

If choosing substitution of b, then:
35.77a%2B13.99%2851-3a%29=643.11
35.77a%2B713.49-41.97a=643.11
%2835.77-41.97%29a=643.11-713.49
-6.2a=-70.38
a=70.38%2F6.2
highlight%28a=11.35%29
and you can solve for b and for 2a, and should check that the solutions work.
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