The equation format I used was y = mx + b. 'Y' is the total, and 'X' is the number of buckets. Because the amount of $2.75 payments depends on how many buckets you use, that is 'M', or the rate of change. 'B' is represented by $4 because that is a one time payment made.
the idea of showing that multiplying by 1 is true because as long as A and B follow the same ratio pattern (ie. 1n:2n is the same as 2n:4n) the statement will always be true