Final answer:
To find the number of different ways of writing 2145 as the sum of two nonzero whole numbers, we need to consider all possible pairs of numbers that add up to 2145. The total number of different ways is equal to the number of pairs, which can be calculated as (2144 + 1) / 2. This gives us 2144 ways.
Step-by-step explanation:
To find the number of different ways of writing 2145 as the sum of two nonzero whole numbers, we need to consider all possible pairs of numbers that add up to 2145. Since the question asks for nonzero whole numbers, we can start by dividing 2145 by 2 to get the largest possible number for the first addend. In this case, 2145 divided by 2 is 1072.5. However, since we are looking for whole numbers, we can round down to 1072.
So, the possible pairs of numbers that add up to 2145 are:
- 1072 and 1073
- 1071 and 1074
- ...
We can continue this pattern until we reach the pair 1 and 2144. Since we are counting pairs, each pair is counted twice (for example, both 1072 and 1073, and 1073 and 1072 are considered different pairs). Therefore, the total number of different ways is equal to the number of pairs which can be calculated as (2144 + 1) / 2. This gives us 1072 pairs. However, we need to consider that these pairs can be rearranged, so the final answer is 2 times the number of pairs, which is 2144 ways. Therefore, the correct answer is c) 2144 ways.