A bank teller has 54 5 dollar bills and 20 dollar bills in her cash drawer. The value of the bills is 780 dollars. How many 5 dollar bills are there?

5x+20(54-x) = 780

To determine the number of 5-dollar bills, you can set up a system of equations based on the given information.

Let's assume x represents the number of 5-dollar bills and y represents the number of 20-dollar bills.

From the given information, we have two equations:
Equation 1: x + y = total number of bills (54 + 20 = 74)
Equation 2: 5x + 20y = total value of bills ($780)

To solve for x (the number of 5-dollar bills), we can use these equations.

First, let's solve Equation 1 for y:
y = total number of bills - x

Substituting this value of y in Equation 2, we get:
5x + 20(total number of bills - x) = $780

Now, we'll simplify this equation:
5x + 20(74 - x) = $780
5x + 1480 - 20x = $780
-15x = -$700

Dividing both sides by -15, we find:
x = 46.67

Since x represents the number of 5-dollar bills and they cannot be in decimal form, we round down to the nearest whole number. Therefore, there are 46 five-dollar bills in the bank teller's cash drawer.