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2015 AMC 10B Problem 4

Problem 4 of 25EasierAlgebra

Four siblings ordered an extra large pizza. Alex ate 15,\frac15, Beth 13,\frac13, and Cyril 14\frac14 of the pizza. Dan got the leftovers. What is the sequence of the siblings in decreasing order of the part of the pizza they consumed?

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Solution

Since 13>14>15,\frac 13 > \frac 14 > \frac 15, we know Beth ate more than Cyril and Cyril ate more than Alex. Thus, those three are in order. The amount Dan ate is 1131415=1360.1- \dfrac 13 - \dfrac 14 - \dfrac 15 = \dfrac{13}{60}. This is greater than 15\frac 15 and less than 14,\frac 14 , so Dan is in between Cyril and Alex. This makes the order Beth, Cyril, Dan, Alex. Thus, the correct answer is C .

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Concepts: fraction

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.