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94. The magazines in a certain library are distributed into three different categories: entertainment, scientific and artistic. The number of scientific magazines in this library is equal to three times the number of entertainment magazines, and the number of scientific magazines exceeds the number of artistic magazines by 25. If the total number of magazines in this library is equal to 353, and if each magazine belongs to only one category, then the difference between the number of artistic magazines and the number of entertainment magazines, in that order, is equal to

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Answer to a math question 94. The magazines in a certain library are distributed into three different categories: entertainment, scientific and artistic. The number of scientific magazines in this library is equal to three times the number of entertainment magazines, and the number of scientific magazines exceeds the number of artistic magazines by 25. If the total number of magazines in this library is equal to 353, and if each magazine belongs to only one category, then the difference between the number of artistic magazines and the number of entertainment magazines, in that order, is equal to

Expert avatar
Maude
4.7
107 Answers
1. Definimos as variáveis:
E (entretenimento), C (científicas), A (artísticas).
2. Convertemos as informações do problema em expressões matemáticas:
C = 3E, C = A + 25, E + C + A = 353.
3. Substituímos C na equação da soma:
E + 3E + (3E - 25) = 353, simplificando para 7E - 25 = 353.
4. Resolvendo para E:
7E = 378 \rightarrow E = 54.
5. Calculamos C e A:
C = 3 \times 54 = 162,
A = 162 - 25 = 137.
6. Encontramos a diferença:
A - E = 137 - 54 = 83.

[Solution] A - E = 83

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