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
