House blend coffee is 50% columbian beans and special blend coffee is 80% columbian beans. how much of each should be used to produce 100kg of a blend that is 68% columbian beans

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