Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 1 - Problem Solving and Critical Thinking - 1.3 Problem Solving - Exercise Set 1.3: 31

Answer

9 ways

Work Step by Step

If we spend $\$4.79$ and pay with a $\$5$ bill, we receive $500-479=21$ cents of change. To make sure we count all the ways we can receive the change, we'll list all possible combinations of all the different coins, sorted by the number of the most valuable coins spent. - (We can't receive 3 dimes, as they're worth more than 21 cents $(3*10>21)$ ). - We can receive 2 dimes and 1 penny $(2*10+1=21)$. - We can receive 1 dime 2 nickels, and a penny $(10+2*5+1=21)$ - We can receive 1 dime, 1 nickel, and 6 pennies $(10 + 5 + 6*1=21)$ - We can receive 1 dime and 11 pennies $(10+11*1=21)$ - We can receive 4 nickels and 1 penny $(4*5+1=21)$ - We can receive 3 nickels and 6 pennies $(3*5+6=21)$ - We can receive 2 nickels and 11 pennies $(2*5+11*1=21)$ - We can receive 1 nickel and 16 pennies $(5+16*1=21)$ - We can receive 21 pennies $(21*1=21)$ This means we can receive the change for the bill in a total of $9$ ways.
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