# Solved: Use the greedy algorithm to make change using ## Problem 54E Chapter 3.1

Discrete Mathematics and Its Applications | 7th Edition

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Problem 54E

Use the greedy algorithm to make change using quarters, dimes, and pennies (but no nickels) for each of the amounts given in Exercise 52. For which of these amounts does the greedy algorithm use the fewest coins of these denominations possible?

Step-by-Step Solution:

Solution: Step 1 :In this problem we have to make change using the quarters, dimes, and pennies (but no nickels).Step 2 : (a) 87 centAns ; 87 cent = 3 quarter + 1 dime + 2 penny=6 coin .’. 87 cent contain only 3 quarter,1 dime and 2 penny.Total 6 coins. This smallest possible number of coins.Step 3 :(b) 49 cent Ans : 49 cent = 1 quarter + 2 dime + 4 penny=7 coins.’. 49 cent contain 1 quarter,2 dime and 4 penny.This is a optimal solution this contain only 7 coins.This smallest possible number of coins.

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##### ISBN: 9780073383095

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Solved: Use the greedy algorithm to make change using

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