Once every week, the 5 members of the band have lunch together. they always order the same number of pizzas and sodas and split the bill evenly. the bill is always $23.70. one day, another friend joined them, and they split the bill evenly 6 ways. how much less did each band member pay?

We can find this out by taking the total (23.70) and dividing it by the 5 band members, getting the number 4.74. Now we do this again, but with the extra band member we get 3.95. Now the last step it 4.74 - 3.95, which is 0.79. So each band member payed 0.79 less than normal.

the solution is 12x-6y