The solution involves the ceiling function.

See http://en.wikipedia.org/wiki/Floor_function

Since I can't write the correct symbol, I will just use [ ] instead.

First, directorz, X = 42 + 36Y should have been written

as B = 36h + 42 where "B" is the amount of the bill and "h" is the number of hours the repairman worked. Of course, X and Y could have been used but, even then, it would have been more appropriate to write it as Y = 42 + 36X since "Y" is usually the dependent variable and "X" independent.

In any case, that is not the correct solution since this problem needs the ceiling function (read the above link) because it states to "round up" for anything over the increment.

Since it wants the increments in 20 minutes, convert the rate from "$36 per hour" to "$12 per twenty minutes" (because there are 3 sets of 20 minutes per hour, $12 per 20min is the same as $36/hour).

Using the variable "m" for "number of minutes", the ceiling of m/20 (denoted as [m/20] ) produces the following:

m=1 gives [1/20]=1

m=2 gives [2/20]=1

m=3 gives [3/20]=1

m=4 gives [4/20]=1

and so on to

m=18 gives [18/20]=1

m=19 gives [19/20]=1

m=20 gives [20/20]=1

m=21 gives [21/20]=2

m=22 gives [22/20]=2

So, you see, it gives the "number of sets of 20 minutes".

In other words, for 1 minute, it is 1 twenty minute period charge, for 2 minutes, it is still 1 twenty minute charge... When you get to 21 minutes, you start charging for a second 20 minute period.

The solution to the problem would be:

B = 12[m/20] + 42

Again, note that the symbol used should have been

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not

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since I don't know what code to put in to get the correct symbol. At one time, a list of codes was posted but I think that topic was archived long ago.