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Consider the problem of creating a particular monetary value using discrete coins, for example: making 15¢ from a 10¢ coin plus a 5¢ coin:denoms = { 1, 5, 10, 25}counts = { 3, 2, 2, 3}result = { 0, 1, 1, 0} // 5 cents + 10 cents = 15 cents For this problem I want to create 29¢ in change, and my cash drawer contains the following coins:denoms = { 1, 5, 10, 25}counts = { 3, 0, 0, 3}result = { 0, 0, 0, 0}(That is: three 1¢ coins and three 25¢ coins are available, but no 5¢ or 10¢ coins at this time, and I have NOT yet begun creating change.)Each step in the change-making process involves taking ONE coin from the counts array and adding it to my result array.Given this setup, which of the following is a valid next step in the process of attempting to make change?Group of answer choicesAdd one 1¢ coin to resultAdd one 5¢ coin to resultAdd one 10¢ coin to resultAdd one 25¢ coin to resultDeclare the 29¢ result impossible

Question

Consider the problem of creating a particular monetary value using discrete coins, for example: making 15¢ from a 10¢ coin plus a 5¢ coin:denoms = { 1, 5, 10, 25}counts = { 3, 2, 2, 3}result = { 0, 1, 1, 0} // 5 cents + 10 cents = 15 cents For this problem I want to create 29¢ in change, and my cash drawer contains the following coins:denoms = { 1, 5, 10, 25}counts = { 3, 0, 0, 3}result = { 0, 0, 0, 0}(That is: three 1¢ coins and three 25¢ coins are available, but no 5¢ or 10¢ coins at this time, and I have NOT yet begun creating change.)Each step in the change-making process involves taking ONE coin from the counts array and adding it to my result array.Given this setup, which of the following is a valid next step in the process of attempting to make change?Group of answer choicesAdd one 1¢ coin to resultAdd one 5¢ coin to resultAdd one 10¢ coin to resultAdd one 25¢ coin to resultDeclare the 29¢ result impossible

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Solution

The valid next step in the process of attempting to make change would be to add one 25¢ coin to the result. This is because you have three 25¢ coins available in your cash drawer, and adding one of them to your result would bring you closer to the target of 29¢. Adding a 1¢ coin would also be valid, but it would not bring you as close to the target as quickly. Adding a 5¢ or 10¢ coin would not be valid, as you do not have any of these coins available. Declaring the 29¢ result impossible would not be valid at this stage, as you still have coins available that can be used to reach the target.

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