How many different Australian coin combinations will make 75 cents? Pls help!
To find the number of different coin combinations that make 75 cents using Australian coins, you can follow these steps:
Step 1: Note down the denominations of Australian coins:
- 1 cent
- 2 cents
- 5 cents
- 10 cents
- 20 cents
- 50 cents
Step 2: Start with the highest denomination and work your way down:
- The biggest coin, 50 cents, cannot be used because it exceeds 75 cents.
- Next, try using 20 cents. Since 75 cents is not a multiple of 20, you can use 3 coins (20 cents x 3 = 60 cents) with 15 cents remaining.
- Now, try using 10 cents. Since 15 cents is immediately less than 10 cents, you cannot use any 10-cent coins.
- Next, try using 5 cents. Since 15 cents is divisible by 5, you can use 3 coins (5 cents x 3 = 15 cents), with no amount remaining.
- Next, try using 2 cents. Since there is no remaining amount, you cannot use any 2-cent coins.
- Lastly, try using 1 cent. Since there is no remaining amount, you cannot use any 1-cent coins.
Step 3: Summarize the combinations:
From the above calculations, there is only one combination of Australian coins that makes 75 cents, which is:
- 20 cents x 3
- 5 cents x 3
Therefore, there is only one different Australian coin combination that will make 75 cents.
To determine the number of different Australian coin combinations that can make 75 cents, we can use a systematic approach. In Australia, there are six different denominations of coins in circulation: 5 cents, 10 cents, 20 cents, 50 cents, 1 dollar, and 2 dollars.
One way to solve this problem is by using a combination of loops in programming. Here's an example of how you can use Python code to solve it:
```python
count = 0
for five_cents in range(0, 16): # The maximum number of 5 cent coins is 15 since more than that exceeds 75 cents
for ten_cents in range(0, 8): # The maximum number of 10 cent coins is 7 since more than that exceeds 75 cents
for twenty_cents in range(0, 4): # The maximum number of 20 cent coins is 3 since more than that exceeds 75 cents
for fifty_cents in range(0, 2): # The maximum number of 50 cent coins is 1 since more than that exceeds 75 cents
for one_dollar in range(0, 1): # The maximum number of 1 dollar coins is 0 or 1 since more than that exceeds 75 cents
for two_dollars in range(0, 1): # The maximum number of 2 dollar coins is 0 or 1 since more than that exceeds 75 cents
total = (five_cents * 0.05) + (ten_cents * 0.1) + (twenty_cents * 0.2) + (fifty_cents * 0.5) + (one_dollar * 1) + (two_dollars * 2)
if total == 0.75:
count += 1
print(f"The number of different Australian coin combinations that can make 75 cents is {count}.")
```
This code uses nested loops to iterate through all possible combinations of coin quantities. It checks each combination to see if the total value equals $0.75. The count is incremented each time a valid combination is found.
Executing this code will give you the answer to your question, which is the number of different coin combinations that can make 75 cents.
There are 18 possible combinations of quarters, dimes and nickels that total 75 cents. Hopefully these are Australian coins!?
1) 3 Quarters
2) 2 Quarters, 2 Dimes, 1 Nickel
3) 2 Quarters, 1 Dime, 3 Nickels
4) 2 Quarters, 5 Nickels
5) 1 Quarter, 5 Dimes
6) 1 Quarter, 4 Dimes, 2 Nickels
7) 1 Quarter, 3 Dimes, 4 Nickels
8) 1 Quarter, 2 Dimes, 6 Nickels
9) 1 Quarter, 1 Dime, 8 Nickels
10) 1 Quarter, 10 Nickels
11) 7 Dimes, 1 Nickel
12) 6 Dimes, 3 Nickels
13) 5 Dimes, 5 Nickels
14) 4 Dimes, 7 Nickels
15) 3 Dimes, 9 Nickels
16) 2 Dimes, 11 Nickels
17) 1 Dime, 13 Nickels
18) 15 Nickels