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

40 kg of 50% Columbian beans required

60 kg of 80% Columbian beans required

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step-by-step explanation: