A company decided to make some gifts containing three different items (A, B and C). In addition to there not being equal quantities of each item, the packages were made by different people who did not pay attention to the instructions given. In the end, it is known that 49 packages contained only item A, 19 contained only item B and 13 contained only item C. And although 22 packages contained items A and B, 24 contained items A and C and 64 contained items B and C. Only 9 packages contained all three items. What was the initial quantity of each item?

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Answer to a math question A company decided to make some gifts containing three different items (A, B and C). In addition to there not being equal quantities of each item, the packages were made by different people who did not pay attention to the instructions given. In the end, it is known that 49 packages contained only item A, 19 contained only item B and 13 contained only item C. And although 22 packages contained items A and B, 24 contained items A and C and 64 contained items B and C. Only 9 packages contained all three items. What was the initial quantity of each item?

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Maude

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Solução: Item A = (somente item A) + (item A e C) + (item A e B) + (todos os três itens) Item A = 49 + 22 + 24 + 9 = 104 Item B = (Item B apenas) + (Item B e C) + (Item A e B) + (Todos os três itens) Item B = 19 + 64 + 22 + 9 = 114 Item C = (Item C apenas) + (Item A e C) + (Item B e C) + (Todos os três itens) Item C = 13 + 24 + 64 + 9 = 110

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