Greatest Integer Function Problem

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The discussion revolves around creating a formula for a phone company's billing structure based on the greatest integer function. The problem highlights the need to account for both integer and non-integer minute usage, specifically addressing how to charge for partial minutes. A suggestion is made to use the floor function to manage rounding down, while also considering a method to round up for billing purposes. The proposed solution involves using a combination of the ceiling function and costs associated with the first and additional minutes. This approach aims to accurately calculate charges regardless of whether the talk time is a whole number or not.
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I just need a push in the right direction for this one.
The problem is: A phone company charges this amount for the first minute and that amount for each additional minute. If someone talks for 3.1 minutes, they are charged for 4 minutes. Make a formula, blah blah blah...
Anyway I'm having trouble with making the equation work for both of these situations: when x is an integer, and when x is not an integer.
I already thought about int(x-.1) but then x could be .01, and it wouldn't be correct.

Any help is appreciated.
 
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You're trying to make a "round up" function. Since you're allowed to use the floor ("round down") function, consider this:

int(x)=-int(-x), x is an integer
int(x)=1-int(-x), otherwise
 
All you need is a + b ceil(x-1), where a is the cost for the first minute and b is the cost of each additional minute.
 

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