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firm has two grades of coffee beans, Grade A and Grade B. 40 kg of Grade A and 45 kg of Grade B are to be mixed and packaged into two types of packets of 1 kg each — economy type and special type. The economy pack consists of beans of Grade A and Grade B in the ratio 1 : 3. The special pack consists of beans of Grade A and Grade B in equal proportion. Find the number of economy and special packs that can be made, using the substitution method.

firm has two grades of coffee beans, Grade A and Grade B. 40 kg of Grade A and 45 kg of Grade B are to be mixed and packaged into two types of packets of 1 kg each — economy type and special type. The economy pack consists of beans of Grade A and Grade B in the ratio 1 : 3. The special pack consists of beans of Grade A and Grade B in equal proportion. Find the number of economy and special packs that can be made, using the substitution method. 

Grade:12

1 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
5 years ago
Dear student
grade A = 40 kg
grade B = 45 kg

Economy = 250 gram grade A + 750 gram grade B
Special = 500 gram grade A + 500 gram grade B

0.25 x + 0.5 y = 40 kg
0.5 x + 0.5 y = 45 kg

x and y are numberof packets of economy and special types

x=10 y=75

total = 85

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