Question 519004
To solve these types of problems, you need to write two equations using what you know.
First, you know that you have two types of bills and a total of 54 bills:
F + T = 54 (F=number of $5 bills, T=number of $20 bills)
Second, you know that the total value of these bills is $780:
5F + 20T = 780
Next you want to get rid of one of the variables (F or T) by plugging one of the equations into the other.  The first equation can be rewritten by subtracting F from both sides:
F + T = 54
T = 54 - F 
Now plug this equation into the second equation for T, and solve for F:
5F + 20T = 780
5F + 20(54-F) = 780
5F + 1080 - 20F = 780
1080 - 15F = 780
-15F = -300
F = 20
So the bank teller has 20 $5 bills.