Aryam has 6 coins that have a total value of 56c. list the coins.
25,10,10,5,5,1
To determine the coins Aryam has, we need to look for possible combinations of coins that add up to a total value of 56c.
There are several ways this can be done, but we'll approach it systematically using a method called "brute force."
Let's start by examining the largest coin possible. Since we're looking for a total value of 56c, the highest value coin cannot be more than 56c. Let's see if Aryam has any 50c coins.
If Aryam has a 50c coin, the remaining total value should be 56c - 50c = 6c.
In this case, Aryam has a 50c coin and 6c remaining. To make up the remaining 6c, Aryam must have a combination of smaller coins.
Now, let's look at the next largest coin possible, which is 20c.
If Aryam has a 20c coin, the remaining total value should be 6c - 20c = -14c.
Since the remaining value is negative, we can conclude that Aryam does not have a 20c coin.
Next, let's move on to the next largest coin, which is 10c.
If Aryam has a 10c coin, the remaining total value should be 6c - 10c = -4c.
Again, since the remaining value is negative, we can conclude that Aryam does not have a 10c coin.
Now, let's move to the next largest coin, which is 5c.
If Aryam has a 5c coin, the remaining total value should be 6c - 5c = 1c.
In this case, Aryam has a 50c coin and a 5c coin, with 1c remaining. Since there is no smaller coin available, Aryam does not have a combination that adds up to the remaining 1c. Therefore, we can conclude that Aryam does not have a 5c coin either.
Finally, let's move to the next largest coin, which is 2c.
If Aryam has a 2c coin, the remaining total value should be 6c - 2c = 4c.
In this case, Aryam has a 50c coin and a 2c coin, with 4c remaining. To make up the remaining 4c, Aryam must have a combination of smaller coins.
Now, let's look at the smallest coin available, which is 1c.
If Aryam has a 1c coin, the remaining total value should be 4c - 1c = 3c.
In this case, Aryam has a 50c coin, a 2c coin, and a 1c coin, with 3c remaining. To make up the remaining 3c, Aryam must have a combination of smaller coins.
Since there are no more coins smaller than 1c, we can conclude that Aryam does not have any additional coins.
So, based on this analysis, the coins Aryam has are:
- 50c
- 2c
- 1c