There are some 1-dollar bills, some 5-dollar bills, and a 20-dollar bill in an envelope. The number of 1 dollar bills is four times the number of the 5 -dollar bills. We randomly pull a bill from the envelope. How many 1-dollar bills are in this envelope if the expected value of the bill pulled is $\$ 2.50$ ? The number of 1-dollar bills is

Step 1 ：Let's denote the number of 1-dollar bills as x and the number of 5-dollar bills as y. According to the problem, x = 4y.

Step 2 ：The expected value of a random variable is the sum of the possible values each multiplied by their respective probabilities. In this case, the possible values are 1, 5, and 20 dollars.

Step 3 ：The probability of drawing a 1-dollar bill is the number of 1-dollar bills divided by the total number of bills. Similarly, the probability of drawing a 5-dollar bill is the number of 5-dollar bills divided by the total number of bills, and the probability of drawing a 20-dollar bill is 1 divided by the total number of bills (since there is only one 20-dollar bill).

Step 4 ：The expected value is given by: E = (1 * P(1-dollar bill) + 5 * P(5-dollar bill) + 20 * P(20-dollar bill)) = 2.5

Step 5 ：Substituting the probabilities and the relationship between x and y into the equation, we get: 2.5 = (1 * x/(x+y+1) + 5 * y/(x+y+1) + 20 * 1/(x+y+1))

Step 6 ：Solving this equation for x, we find that x = 20.

Step 7 ：Final Answer: The number of 1-dollar bills in the envelope is \(\boxed{20}\).