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2010 AMC 10A Problem 4

Problem 4 of 25EasierNumber TheoryArithmetic

A book that is to be recorded onto compact discs takes 412412 minutes to read aloud. Each disc can hold up to 5656 minutes of reading. Assume that the smallest possible number of discs is used and that each disc contains the same length of reading. How many minutes of reading will each disc contain?

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Solution

Note that 7⋅56=3927 \cdot 56 = 392 and 8⋅56=448,8 \cdot 56 = 448, which means that the minimum number of discs needed is 8.8. Then the minutes of reading that each disc contains is 412÷8=51.5. 412 \div 8 = 51.5. Thus, B is the correct answer.
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