**X** will represent the number of $10 bills. **Y** will represent the number of $20 bills.

Step 1: Set up a system of equations. What do we know from the information given? Well we know that Jeannie has $4370 total made up of a certain amount of $10 bills (X) and a certain amount of $20 bills (Y). This is represented as:
**10X + 20Y = 4370**. We also know that Jeannie has a total of 273 actual bills. Some of them are $10 bills and some are $20 bills. This is represented as:
**X + Y = 273**.

Step 2: Solve for one of the variables first. To do this, you will need to plug one of the equations into the other equation. Let's solve for X first. The equation X + Y = 273 can be simplified to Y = 273 - X. Now, this can be plugged into the very first equation:

**10X + 20(273 - X) = 4370**

10X + 5460 - 20X = 4370

-10X + 5460 = 4370

-10X = -1090

** X = 109** ; **So there are 109 $10 bills.**

Now we can plug the solution for X into any of the equations to find Y. Let's plug it into the most simple equation: X + Y = 273.

109 + Y = 273

** Y = 164** ; **
so there are 164 $20 bills.**

To check your solution for accuracy, plug your results for both X and Y into the other equation:

10X + 20Y = 4370

10(109) + 20(164) = 4370

1090 + 3280 = 4370

4370 = 4370. This is true, thus your X and Y results are correct.