Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 3 - Section 3.1 - Algorithms - Exercises - Page 204: 55

Answer

a) 2 quarters and 1 penny. b) 2 quarters, 1 dime, and 9 pennies. c) 3 quarters and 1 penny. d) 2 quarters and 1 dime.

Work Step by Step

a) 51 cents: Start with the largest denomination, the quarter (25 cents). We can use two quarters, leaving 1 cent remaining. Move to the next largest denomination, the penny (1 cent). We can use one penny to make a total of 51 cents. The solution is 2 quarters and 1 penny. b) 69 cents: Start with the largest denomination, the quarter (25 cents). We can use two quarters, leaving 19 cents remaining. Move to the next largest denomination, the dime (10 cents). We can use one dime, leaving 9 cents remaining. Move to the next largest denomination, the penny (1 cent). We can use all 9 remaining cents, which requires 9 pennies. The solution is 2 quarters, 1 dime, and 9 pennies. c) 76 cents: Start with the largest denomination, the quarter (25 cents). We can use three quarters, leaving 1 cent remaining. Move to the next largest denomination, the penny (1 cent). We can use one penny to make a total of 76 cents. The solution is 3 quarters and 1 penny. d) 60 cents: Start with the largest denomination, the quarter (25 cents). We can use two quarters, leaving 10 cents remaining. Move to the next largest denomination, the dime (10 cents). We can use one dime, leaving 0 cents remaining. The solution is 2 quarters and 1 dime.
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