Question 1197122
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The key to finding the right answer to a problem like this is to make sure you have found all the possible combinations (and have not repeated any), using a completely logical process.  The responses from the other tutors show the correct combinations and the correct number of combinations; but it is not clear in their responses whether they used a process that definitely found all the combinations.<br>
Here is how I would organize the work for finding the answer.<br>
The amount of change is 24 cents.  So it must be in pennies, nickels, and dimes.<br>
The dimes and nickels together make an amount that is a multiple of 5 cents.  To make 24 cents, the number of pennies needs to be 4, 9, 14, 19, or 24.<br>
For each possible number of pennies, the remaining amount will be a multiple of 5 cents.  Since a dime is the same as 2 nickels, the number of ways to make 24 cents total using a given number of pennies is determined by the possible numbers of dimes.<br>
(1) 4 pennies; 20 cents left; there can be 0, 1, or 2 dimes.  3 ways
(2) 9 pennies; 15 cents left; there can be 0 or 1 dimes.  2 ways
(3) 14 pennies; 10 cents left; there can be 0 or 1 dimes.  2 ways
(4) 19 pennies; 5 cents left; there can only be 0 dimes.  1 way
(5) 24 pennies; 0 cents left; there can only be 0 dimes.  1 way<br>
ANSWER: 3+2+2+1+1 = 9 ways<br>