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A coffee house blended 16 pounds of espresso flavored coffee beans with 10 pounds of vanilla flavored coffee b?

• A coffee house blended 16 pounds of espresso flavored coffee beans with 10 pounds of vanilla flavored coffee beans. The 26 pound mixture cost $229. A second mixture included 14 pounds of espresso flavored coffee beans and 11 pounds of vanilla flavored coffee beans. The 25 pound mixture cost $219.50. Find the cost per pound of the espresso and vanilla flavored coffee beans.

• Answer:

  Espresso = $9 per pound and Vanilla = $8.50 per pound. Set up and solve a pair of simultaneous equations. Let the price of espresso be E and vanilla V 16E + 10V = 229 = Equation 1 16 pounds of espresso flavored coffee beans with 10 pounds of vanilla flavored coffee beans. The 26 pound mixture cost $229 14E + 11 V = 219.50 = Equation 2 14 pounds of espresso flavored coffee beans and 11 pounds of vanilla flavored coffee beans. The 25 pound mixture cost $219.50. Lets use the ELIMINATION method and eliminate V 16E + 10V = 229 = Equation 1 14E + 11 V = 219.50 = Equation 2 Eliminate V by Multiplying Equation 1 by 11 and Equation 2 by 10. This will then make the V coefficients identicall 176E + 110V = 2519 (Eq 1*11) 140E + 110V = 2195 (Eq 2*10) Now eliminate V by subtracting the bottom equation from the top (176 - 140)E + (110 - 110)V = (2519 - 2195) Simplify 36E = 324 E = 324/36 E = $9 But we know that 16E + 10 V = 229 As E = 9 144 + 10V = 229 10V = 85 V = 85/10 = $8.50 14 pounds @ $9 per pound + 11 pounds @ $8.50 per pound totals $126 + $93.50 = $219.50 therefore correct