Let us say that,
x = mass of 50% Columbian beans required
y = mass of 80% Columbian beans required
To solve this problem, we set up two mass balance equations:
Overall mass balance: 100 = x + y
x = 100 – y ---> 1
Coffee mass balance: 0.68 (100) = 0.50 x + 0.80 y
68 = 0.50 x + 0.80 y ---> 2
Combining equations 1 and 2:
68 = 0.50 (100 – y) + 0.80 y
68 = 50 – 0.50 y + 0.80 y
18 = 0.30 y
y = 60 kg
Calculating for x using equation 1:
x = 100 – y
x = 100 – 60
x = 40 kg
Answer:
40 kg of 50% Columbian beans required
60 kg of 80% Columbian beans required
