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.
10/7/2013

Angela C.