Answer:
8 lb of French Roast and 12 lb of City Roast coffee
Step-by-step explanation:
In this scenario, we identify two variables: the weight of City Roast coffee (denote as "C") and that of French Roast coffee (denote as "F")
The first equation we create pertains to the overall weight of the coffee (20 lb total), represented by C and F as follows:
first equation C + F = 20
Subsequently, we derive another equation regarding the mixture's cost. Each pound of City Roast costs $7.80, so for C pounds, the cost becomes $7.80 * C
For the French Roast—priced at $8.10 per pound—we deduce that F pounds will cost $8.10 * F
The total of these costs should equal the desired total for the 20 lb blend: $7.92 * 20 = $158.4
We format the total cost equation as follows:
$7.80 * C + $8.10 * F = $158.4
Next, we use the first equation to express one variable in terms of the other, allowing us to solve for "C":
C + F = 20
C = 20 - F
We then replace "C" in the second equation with this expression:
7.80 (20 - F) + 8.10 F = 158.4
7.80 * 20 - 7.80 F + 8.10 F = 158.4
Combining the F terms results in + 0.3 F
156 + 0.3 F = 158.4
Isolating F results in:
0.3 F = 158.4 - 156 = 2.4
Dividing both sides by 0.3 yields:
F = 2.4 / 0.3 = 8
This indicates that we need 8 pounds of French Roast coffee.
Consequently, the remainder (12 lb) should consist of the City Roast.
