SOLUTION: A coffee manufacturer sells a 10-pound package of coffee that consists of three flavors of coffee. Vanilla-flavored coffee costs $12 per pound, hazelnut-flavored coffee costs $13.5

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Question 1115647: A coffee manufacturer sells a 10-pound package of coffee that consists of three flavors of coffee. Vanilla-flavored coffee costs $12 per pound, hazelnut-flavored coffee costs $13.50 per pound, and mocha-flavored coffee costs $15 per pound. The cost of the 10 pound package is $138. The package contains the same amount of hazelnut coffee as mocha coffee. How many pounds of each type of coffee are in the package?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
v Vanilla
h Hazelnut
m Mocha

h=m=x
x for each of Hazelnut and of Mocha

system%28v%2B2x=10%2C12v%2B%2813.5%2B15%29x=138%29

system%28v%2B2x=10%2C12v%2B28.5x=138%29

If trying to eliminate v to get x,
system%2812v%2B24x=120%2C12v%2B28.5x=138%29

4.5x=18

highlight%28x=4%29------------4 pounds of hazelnut and 4 pounds of mocha.

This leaves highlight%28v=2%29-----------2 pounds of vanilla.

Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
.

                Again, typical problem to solve using  SINGLE  unknown. 


Let x = amount of hazelnut (in pounds).

Then the amount of mocha coffee is the same x pounds.

Then the amount of vanilla-flavored coffee is (10-2x) pounds.


The money equation is

12*(10-2x) + 13.50x + 15x = 138,   or


120 - 24x + 28.5x = 138,

4.5x = 138 - 120 = 18  ====>  x = 18%2F4.5 = 4 pounds.


Answer.  4 pounds of hazelnut;  4 pounds of mocha coffee;  and  2 pounds of vanilla-flavored coffee.

Solved.