Question

A coffee house blended 18 pounds of espresso flavored coffee beans with 17 pounds of vanilla flavored coffee beans. The 35 pound mixture cost $306.50. A second mixture included 19 pounds of espresso flavored coffee beans and 15 pounds of vanilla flavored coffee beans. The 34 pound mixture cost $298.50. Find the cost per pound of the espresso and vanilla flavored coffee beans.

Answer 1

Answer:

the price of the vanilla flavored coffee per pound is $8.50

the price of the espresso flavored coffee per pound is $9.00

Step-by-step explanation:

Let's give letters to the unknowns, so we can generate equations easily:

cost of espresso coffee beans per pound:  "E"

cost of vanilla flavored coffee beans per pound : "V"

Now, the first statement:

18 pounds of E plus 17 pounds of V cost $306.50, can be written as:

18 E + 17 V = 306.5

The second statement:

19 pounds of E plus 15 pounds of V cost $298.50, can be written as:

19 E + 15 V = 298.5

Now, in order to solve this system of linear equations we can use substitution for example:

E = (306.5 -17 V)/18

and use this expression to substitute for E in the second equation:

19  (306.5 - 17 V)/ 18 + 15 V = 298.5

multiplying by 18 on both sides to eliminate denominators, we get:

19 (306.5 - 17 V) + 270 V = 5373

5823.5 - 323 V +270 V = 5373

5823.5 - 53 V = 5373

5823.5 - 5373 = 53 V

450.5 = 53 V

V = 8.5

Therefore the price of the vanilla flavored coffee per pound is $8.50

Now we use this found value in the substitution equation:

E = (306.5 -17 V)/18

E = (306.5 - 17 (8.5))/18

E = 9

Therefore the price of the espresso flavored coffee per pound is $9.00