Final answer:
The correct number of different pairs of whole numbers that sum up to 99 is 49, obtained by starting with the numbers 0 and 99 and working up to the center pair 49 and 50, then subtracting this middle pair.
Step-by-step explanation:
To determine how many pairs of whole numbers have a sum of 99, we start with the smallest whole number, which is 0, and pair it with 99 (0+99). Then we increase the first number to 1 and decrease the second number correspondingly to maintain the sum of 99 (1+98). This process continues until we reach a pair where both numbers are the same, in this case, 49 and 50.
The pairs from 0+99 to 49+50 are 50 pairs. However, we are looking for pairs of different whole numbers with a sum of 99. We must subtract the one pair where both numbers are the same (49+50), resulting in a total of 50 - 1 = 49 different pairs. Option c (45 pairs) is the closest choice, but it is incorrect. The correct number of pairs is actually 49, which is not listed among the options provided.