Two boxes A and B were filled with coffee and chicory. The mixture in A is in the ratio 5 : 3 and in B is in the ratio 7 : 3. What quantity must be taken from each box to form a mixture, which shall contain 6 kg of coffee and 3 kg of chicory (in kg respectively)?

Let a kg from A and b kg from B. From A: coffee = (5/8)a, chicory = (3/8)a. From B: coffee = (7/10)b, chicory = (3/10)b. Total coffee: (5/8)a + (7/10)b = 6. Total chicory: (3/8)a + (3/10)b = 3. Multiply coffee equation by 40: 25a + 28b = 240. Multiply chicory equation by 40: 15a + 12b = 120. Solving: From chicory eq, 5a + 4b = 40, so a = (40-4b)/5. Substituting: 25(40-4b)/5 + 28b = 240 gives 200 - 20b + 28b = 240, so 8b = 40, b = 5. Then a = 4.