To solve this problem, we can create a system of equations based on the given information.
Let's assume the number of ten-dollar bills is represented by 't', the number of five-dollar bills is represented by 'f', and the number of one-dollar bills is represented by 'o'.
We are given the following information:
1. Johnny has 38 bills in total. Therefore, we can write the equation:
t + f + o = 38 -- Equation 1
2. Johnny has twice as many fives as tens. Since the number of fives is twice the number of tens, we can write the equation:
f = 2t -- Equation 2
3. Johnny has three more ones than fives. We can write the equation:
o = f + 3 -- Equation 3
Now, we need to solve this system of equations to find the values of t, f, and o.
To start, we can substitute Equation 2 into Equation 1 and Equation 3:
t + (2t) + o = 38 (substituting f from Equation 2 into Equation 1)
o = (2t) + 3 (substituting f from Equation 2 into Equation 3)
Combining like terms in the first equation:
3t + o = 38 -- Equation 4
Now, we have a system of two equations:
3t + o = 38 -- Equation 4
o = 2t + 3 -- Equation 5
From Equation 5, we can substitute o in Equation 4 with (2t + 3):
3t + 2t + 3 = 38
5t + 3 = 38
5t = 38 - 3
5t = 35
t = 35/5
t = 7
So, Johnny has 7 ten-dollar bills.
Now, let's substitute the value of t into Equation 2 to find the value of f:
f = 2t
f = 2(7)
f = 14
Therefore, Johnny has 14 five-dollar bills.
Finally, let's substitute the value of f into Equation 3 to find the value of o:
o = f + 3
o = 14 + 3
o = 17
Hence, Johnny has 17 one-dollar bills.
In conclusion, Johnny has 7 ten-dollar bills, 14 five-dollar bills, and 17 one-dollar bills.