2010 AMC 10A Problem 4

Below is the professionally curated solution for Problem 4 of the 2010 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2010 AMC 10A solutions, or check the answer key.

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Concepts:divisibility estimation

Difficulty rating: 1030

A book that is to be recorded onto compact discs takes $412$ minutes to read aloud. Each disc can hold up to $56$ 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?

$50.2$

$51.5$

$52.4$

$53.8$

$55.2$

Solution:

Note that $7 \cdot 56 = 392$ and $8 \cdot 56 = 448,$ which means that the minimum number of discs needed is $8.$

Then the minutes of reading that each disc contains is $412 \div 8 = 51.5.$

Thus, B is the correct answer.

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