Asked by Samantha Blair
                There are 3 denominations of bills in a wallet: $1, $5, and $10. There are 5 fewer $5 dollar bills than $1 dollar bills. There are half as many $10 dollar bills as $5 dollar bills. If there is $115 altogether, find the number of each type of bill in the wallet.
            
            
        Answers
                    Answered by
            Samantha Blair
            
    No.
    
                    Answered by
            GPT 3.5
            
    Let's first assign variables to the unknown quantities. Let's call the number of $1 bills "x," the number of $5 bills "y," and the number of $10 bills "z."
From the first statement, we know that there are 5 fewer $5 bills than $1 bills.
So, the number of $5 bills is y = x - 5.
From the second statement, we know that there are half as many $10 bills as $5 bills.
So, the number of $10 bills is z = (1/2)y = (1/2)(x - 5) = (x - 5)/2.
From the third statement, we know that there is altogether $115.
The total value of the $1 bills is 1 * x = x.
The total value of the $5 bills is 5 * y = 5 * (x - 5) = 5x - 25.
The total value of the $10 bills is 10 * z = 10 * (x - 5)/2 = 5(x - 5).
So the equation is x + 5x - 25 + 5(x - 5) = 115.
This simplifies to x + 5x - 25 + 5x - 25 = 115.
Combining like terms, we get 11x - 50 = 115.
Adding 50 to both sides, we get 11x = 165.
Dividing both sides by 11, we get x = 15.
So, there are x = <<15=15>>15 $1 bills in the wallet.
Therefore, there are y = x - 5 = 15 - 5 = <<15-5=10>>10 $5 bills in the wallet.
And there are z = (x - 5)/2 = (15 - 5)/2 = <<15-5=10>>10/2 = <<10/2=5>>5 $10 bills in the wallet. Answer: \boxed{15, 10, 5}.
    
From the first statement, we know that there are 5 fewer $5 bills than $1 bills.
So, the number of $5 bills is y = x - 5.
From the second statement, we know that there are half as many $10 bills as $5 bills.
So, the number of $10 bills is z = (1/2)y = (1/2)(x - 5) = (x - 5)/2.
From the third statement, we know that there is altogether $115.
The total value of the $1 bills is 1 * x = x.
The total value of the $5 bills is 5 * y = 5 * (x - 5) = 5x - 25.
The total value of the $10 bills is 10 * z = 10 * (x - 5)/2 = 5(x - 5).
So the equation is x + 5x - 25 + 5(x - 5) = 115.
This simplifies to x + 5x - 25 + 5x - 25 = 115.
Combining like terms, we get 11x - 50 = 115.
Adding 50 to both sides, we get 11x = 165.
Dividing both sides by 11, we get x = 15.
So, there are x = <<15=15>>15 $1 bills in the wallet.
Therefore, there are y = x - 5 = 15 - 5 = <<15-5=10>>10 $5 bills in the wallet.
And there are z = (x - 5)/2 = (15 - 5)/2 = <<15-5=10>>10/2 = <<10/2=5>>5 $10 bills in the wallet. Answer: \boxed{15, 10, 5}.
                    Answered by
            GPT 3.5
            
    Apologies for the incorrect solution. Let's try again.
Let's assign variables to the unknown quantities. Let's call the number of $1 bills "x," the number of $5 bills "y," and the number of $10 bills "z."
From the first statement, we know that there are 5 fewer $5 bills than $1 bills.
So, the number of $5 bills is y = x - 5.
From the second statement, we know that there are half as many $10 bills as $5 bills.
So, the number of $10 bills is z = (1/2)y = (1/2)(x - 5) = (x - 5)/2.
From the third statement, we know that there is altogether $115.
The total value of the $1 bills is 1 * x = x.
The total value of the $5 bills is 5 * y = 5 * (x - 5) = 5x - 25.
The total value of the $10 bills is 10 * z = 10 * (x - 5)/2 = 5(x - 5).
So the equation is x + 5x - 25 + 5(x - 5) = 115.
This simplifies to x + 5x - 25 + 5x - 25 = 115.
Combining like terms, we get 11x - 50 = 115.
Adding 50 to both sides, we get 11x = 165.
Dividing both sides by 11, we get x = 15.
So, there are x = 15 $1 bills in the wallet.
Therefore, there are y = x - 5 = 15 - 5 = 10 $5 bills in the wallet.
And there are z = (x - 5)/2 = (15 - 5)/2 = 10/2 = 5 $10 bills in the wallet.
Answer: 15 $1 bills, 10 $5 bills, and 5 $10 bills.
    
Let's assign variables to the unknown quantities. Let's call the number of $1 bills "x," the number of $5 bills "y," and the number of $10 bills "z."
From the first statement, we know that there are 5 fewer $5 bills than $1 bills.
So, the number of $5 bills is y = x - 5.
From the second statement, we know that there are half as many $10 bills as $5 bills.
So, the number of $10 bills is z = (1/2)y = (1/2)(x - 5) = (x - 5)/2.
From the third statement, we know that there is altogether $115.
The total value of the $1 bills is 1 * x = x.
The total value of the $5 bills is 5 * y = 5 * (x - 5) = 5x - 25.
The total value of the $10 bills is 10 * z = 10 * (x - 5)/2 = 5(x - 5).
So the equation is x + 5x - 25 + 5(x - 5) = 115.
This simplifies to x + 5x - 25 + 5x - 25 = 115.
Combining like terms, we get 11x - 50 = 115.
Adding 50 to both sides, we get 11x = 165.
Dividing both sides by 11, we get x = 15.
So, there are x = 15 $1 bills in the wallet.
Therefore, there are y = x - 5 = 15 - 5 = 10 $5 bills in the wallet.
And there are z = (x - 5)/2 = (15 - 5)/2 = 10/2 = 5 $10 bills in the wallet.
Answer: 15 $1 bills, 10 $5 bills, and 5 $10 bills.
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