an envelope contains 20 bills in denominations of $1,$5,$10, there are two times as many $5 bills as there are$10 bills. the total of the envelope is $54. how many of each bill do i have

let number of tens be x

then number of fives = 2x
number of ones = 20 - 3x

10x + 5(2x) + 1(20-3x) = 54

solve for x, sub back into my definitions

(should get 2 tens, 4 fives, and 14 ones)

To find out how many of each bill you have, we can set up a system of equations based on the given information.

Let's assume the number of $10 bills is x. Since there are twice as many $5 bills, the number of $5 bills would be 2x.

Now, we can establish the equation for the total amount of money in the envelope. The value of the $1 bills can be calculated by multiplying the number of $1 bills (20 - x - 2x) by $1. The value of the $5 bills is the number of $5 bills (2x) multiplied by $5. The value of the $10 bills is the number of $10 bills (x) multiplied by $10. So, we have the equation:

(20 - x - 2x)(1) + (2x)(5) + (x)(10) = 54

Now, we can simplify and solve the equation:

20 - 3x + 10x + x = 54
-3x + 11x + x = 54 - 20
9x = 34
x = 34/9

To find the values of each bill, substitute the value of x back into the equation:

Number of $1 bills = 20 - (34/9) - 2(34/9)
Number of $5 bills = 2(34/9)
Number of $10 bills = 34/9

Now, you can calculate these values to find the exact number of each bill you have.