Use pennies, nickles, dimes, and quarters. Make a combination that is worth one dollar where you have one of some kind of coin, double of another, double that of another, and some number of the last coin.
To solve this problem, we can break it down step by step and try different combinations until we find the solution.
Step 1: Determine the range of values for each coin.
- Pennies (1 cent each)
- Nickels (5 cents each)
- Dimes (10 cents each)
- Quarters (25 cents each)
Step 2: Start with one penny and determine the remaining value needed (100 cents - 1 cent = 99 cents).
Step 3: Choose a coin to double. Let's choose the nickels. If we double the value of a nickel (5 cents * 2 = 10 cents), we still have 99 - 10 = 89 cents remaining.
Step 4: Choose another coin to double. Let's choose the dimes. If we double the value of a dime (10 cents * 2 = 20 cents), we still have 89 - 20 = 69 cents remaining.
Step 5: Determine the number of quarters needed. Since each quarter is worth 25 cents, 69 cents divided by 25 cents equals 2 remainder 19.
Step 6: Based on the remainder, we determine the number of dimes needed. 19 cents divided by 10 cents equals 1 remainder 9.
Step 7: Finally, we calculate the number of nickels needed based on the remaining value of 9 cents. 9 cents divided by 5 cents equals 1 remainder 4.
Therefore, the combination that meets the criteria of having one of some kind of coin (penny), double of another (nickel), double that of another (dime), and some number of the last coin (quarters) is:
- 1 penny (1 cent)
- 2 nickels (10 cents)
- 2 dimes (20 cents)
- 1 quarter (25 cents)
Adding up the values of each coin: 1 + 2*5 + 2*10 + 25 = 1 + 10 + 20 + 25 = 56 cents.
So, this combination does not add up to one dollar. We need to adjust our solution.
Let's try another combination:
- 1 quarter (25 cents)
- 2 dimes (20 cents)
- 2 nickels (10 cents)
- 9 pennies (9 cents)
Adding up the values of each coin: 25 + 2*10 + 2*5 + 9 = 25 + 20 + 10 + 9 = 64 cents.
Again, this combination does not add up to one dollar.
We need to try another combination:
- 1 quarter (25 cents)
- 2 dimes (20 cents)
- 9 nickels (45 cents)
- 3 pennies (3 cents)
Adding up the values of each coin: 25 + 2*10 + 9*5 + 3 = 25 + 20 + 45 + 3 = 93 cents.
Unfortunately, this combination doesn't equal one dollar either.
We can continue iterating through different combinations until we find the solution that adds up to one dollar:
- 2 quarters (50 cents)
- 3 dimes (30 cents)
- 8 nickels (40 cents)
- 2 pennies (2 cents)
Adding up the values of each coin: 2*25 + 3*10 + 8*5 + 2 = 50 + 30 + 40 + 2 = 122 cents.
This combination is incorrect as well.
At this point, we can conclude that there is no combination of one penny, double of another coin, double of another coin, and some number of the last coin, using pennies, nickels, dimes, and quarters, that adds up to exactly one dollar.