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# Use the greedy algorithm to make change using quarters. ISBN: 9780073383095 37

## Solution for problem 55E Chapter 3.1

Discrete Mathematics and Its Applications | 7th Edition

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Problem 55E

Use the greedy algorithm to make change using quarters. dimes, and pennies (but no nickels) for each of the amounts given in Exercise 53. For which of these amounts does the greedy algorithm use the fewest coins of these denominations possible?

Step-by-Step Solution:

Step 1 :

In this problem we have to make change using the quarters, dimes, and pennies (but no nickels).

Step 2 :

(a) 51 cent

Ans ; 51 cent = 2 quarter + 0 dime + 1 penny=3 coin

.’. 51 cent contain only 2 quarter and 1 penny

This smallest possible number of coins.

Step 3 :

(b) 69 cent

Ans : 69 cent = 2 quarter + 1 dime + 9 penny=12 coins

.’. 69 cent contain 2 quarter,1 dime and 9 penny.

Total 12 coins.

This is not a optimal solution because 1 quarter, 4 dimes and 4 penny provides a solution with only 9 coins,

Step 4 of 5

Step 5 of 5

##### ISBN: 9780073383095

Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. This full solution covers the following key subjects: Algorithm, amounts, use, these, greedy. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. Since the solution to 55E from 3.1 chapter was answered, more than 240 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. The full step-by-step solution to problem: 55E from chapter: 3.1 was answered by , our top Math solution expert on 06/21/17, 07:45AM. The answer to “Use the greedy algorithm to make change using quarters. dimes, and pennies (but no nickels) for each of the amounts given in Exercise 53. For which of these amounts does the greedy algorithm use the fewest coins of these denominations possible?” is broken down into a number of easy to follow steps, and 41 words.

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