Janette went to Tire Mart and paid $122.57 per tire for 4 tires and a flat rate fee for installation for a total of $555.28 before taxes. Monique went to Fast Wheels and paid $136.71 per tire for 4 tires and a flat rate fee for installation for a total of $585.34 before taxes. The difference in the amount that they paid in installation charges is $__

To find the difference in the amount they paid in installation charges, we need to subtract the total amount Monique paid from the total amount Janette paid.

Janette paid $555.28 - $122.57 x 4 = $555.28 - $490.28 = $65 in installation charges.

Monique paid $585.34 - $136.71 x 4 = $585.34 - $546.84 = $38.50 in installation charges.

The difference in the amount they paid in installation charges is $65 - $38.50 = $<<65-38.5=26.50>>26.50. Answer: \boxed{26.50}.