Let's solve this problem step by step.
Let's assign variables to the number of each type of bill:
- Let's say the number of $10 dollar bills is "x."
- Based on the given information, the number of $5 dollar bills would be "x + 1" (one more than the number of $10 dollar bills).
- Additionally, the number of one dollar bills would be "2(x + 1) = 2x + 2" (two more than the number of $5 dollar bills).
Now, let's calculate the total value of all the bills:
- The value of $10 dollar bills is 10 * x dollars.
- The value of $5 dollar bills is 5 * (x + 1) dollars.
- The value of one dollar bills is 1 * (2x + 2) dollars.
The total value of the bills Tanya has is given as $40.
Therefore, we can set up the following equation:
10x + 5(x + 1) + 1(2x + 2) = 40
Simplifying the equation:
10x + 5x + 5 + 2x + 2 = 40
17x + 7 = 40
17x = 33
x = 33 / 17 (approximately 1.94)
Since Tanya cannot have a fraction of a bill, we know that the number of $10 dollar bills, x, is 1 (rounded down from approximately 1.94).
So, Tanya has:
- 1 $10 dollar bill,
- 1 + 1 = 2 $5 dollar bills,
- 2(1 + 1) = 4 one dollar bills.
Therefore, Tanya has 1 $10 bill, 2 $5 bills, and 4 $1 bills.