Percentage Rounding Error - Part 2
Samuel is taking inventory at his pet store. Rounded to the nearest integer, of his pets are cats, of his pets are dogs, and the rest constitute . How many possibilities are there for ?
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1 solution
To sum the rounded values of 3 numbers that sum to 100, the error on each number is strictly less than 0.5. So the total error will be strictly inside the 100±(3•0.5), or 98.5 to 101.5 range. There are only 3 integers in this range that can represent the final rounded sum, respectively 99,100, and 101.