SOLUTION: If you spend ​$​ 9.76 in how many ways can you receive change from a ​ten dollar ​bill?

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Question 1197122: If you spend ​$​ 9.76 in how many ways can you receive change from a ​ten dollar ​bill?
Found 3 solutions by ewatrrr, MathLover1, greenestamps:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi
If you spend ​$​ 9.76 in how many ways can you receive change from a ​ten dollar ​bill?
 24 cents in change: using pennies, nickels and dimes

 Using Pennies:       
     24 pennies
 Using Nickel(s) along with pennies
    1N and 19 pennies 
    2N and 14 pennies
    3N and  9 pennies
    4N and  4 pennies
 Using Dimes(s) along with pennies
    1D and 14pennies
    2D and 4 pennies
 Using Dimes(s) and Nickel(s) along with pennies
   1D and 1N and 9 pennies
   1D and 2N and 4 pennies

Wish You the Best in your Studies.


Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The difference will be 10.00-9.76=0.24.
That is 24+cents.
There are coins: 1,5,10+and 25 cents. You cannot use a quarter, it’s more than 24 cents.

We list all the possible options.
penny: 1%2A24=24
dimes and pennies: 10%2B14=24
dimes and pennies: 10%2B10%2B4=24
dimes, nickels, and pennies: 10%2B5%2B5%2B4=24
dimes, nickels, and pennies: 10%2B5%2B9=24
nickels and pennies: 5%2B5%2B5%2B5%2B4=24
nickels and pennies: 5%2B5%2B14=24
nickels and pennies: 5%2B19=24
nickels and pennies: 5%2B5%2B5%2B9=24

==>+9+ ways

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


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.

Here is how I would organize the work for finding the answer.

The amount of change is 24 cents. So it must be in pennies, nickels, and dimes.

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.

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.

(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

ANSWER: 3+2+2+1+1 = 9 ways