Kayla has 5 quarters, 3dimes,2 nickles and 5 pennies. How many different combonations of coins can she make to have 0.50?
q+q
q+2d+n
q+2d+5p
q+d+2n+5p
To find the number of different combinations of coins that Kayla can make to have a total value of $0.50, we can use the concept of counting coin combinations.
First, let's convert the values of the coins to cents:
- 5 quarters: 5 * 25 cents = 125 cents
- 3 dimes: 3 * 10 cents = 30 cents
- 2 nickels: 2 * 5 cents = 10 cents
- 5 pennies: 5 * 1 cent = 5 cents
Now, let's list all the possible combinations of coins that can add up to $0.50 (or 50 cents).
One approach to solving this problem is to use a brute force method and try out all possible combinations. Here's one way to do it:
1. Start with the largest denomination first (quarters). Since we have 5 quarters, let's consider the number of quarters from 0 to 5 in our combinations.
- 0 quarters: We need to make 50 cents using the remaining coins (dimes, nickels, and pennies).
- 1 quarter: We need to make 25 cents using the remaining coins.
- 2 quarters: We need to make 0 cents (since 50 - 2 * 25 = 0) using the remaining coins.
- 3 quarters: This is not possible since 50 - 3 * 25 = -25, which is less than 0.
- 4 quarters: This is not possible since 50 - 4 * 25 = 0.
2. For each number of quarters, we move on to the next denomination (dimes) and consider the number of dimes from 0 to 3 (the maximum number of available dimes).
- 0 dimes: We need to make 50 cents using the remaining coins (nickels and pennies).
- 1 dime: We need to make 40 cents using the remaining coins.
- 2 dimes: We need to make 30 cents using the remaining coins.
- 3 dimes: This is not possible since 50 - 3 * 25 - 3 * 10 = -5, which is less than 0.
3. For each number of quarters and dimes, we move on to the next denomination (nickels).
- 0 nickels: We need to make 50 cents using the remaining coins (pennies).
- 1 nickel: We need to make 45 cents using the remaining coins.
- 2 nickels: We need to make 40 cents using the remaining coins.
- 3 nickels: We need to make 35 cents using the remaining coins.
- 4 nickels: We need to make 30 cents using the remaining coins.
4. Finally, for each number of quarters, dimes, and nickels, we consider the number of pennies required to make up the remaining amount.
- 0 pennies: We need to make 50 cents, which is not possible.
- 1 penny: We need to make 49 cents, which is not possible.
- 2 pennies: We need to make 48 cents, which is not possible.
- 3 pennies: We need to make 47 cents, which is not possible.
- ...
- 50 pennies: We need to make 0 cents, which is possible.
By going through these steps, we can find all the possible combinations of coins that add up to 50 cents. In this case, there are 6 different combinations:
1. 1 quarter, 2 dimes, 4 nickels, 5 pennies
2. 1 quarter, 5 dimes, 2 nickels, 5 pennies
3. 2 quarters, 1 dime, 3 nickels, 5 pennies
4. 3 quarters, 0 dimes, 2 nickels, 5 pennies
5. 4 quarters, 3 nickels, 5 pennies
6. 10 nickels, 5 pennies
So, Kayla can make 6 different combinations of coins to have a total value of $0.50.