How many pairs of Whole numbers have a sum of 40

How many pairs of Whole numbers have a sum of 40

The correct answer and explanation is:

To find how many pairs of whole numbers have a sum of 40, we need to understand a few key points:

✅ Correct Answer: 41 pairs

🔍 Explanation (300 words):

Whole numbers are non-negative integers, meaning they include 0, 1, 2, 3, … (but not negative numbers or decimals).

When we are asked how many pairs of whole numbers have a sum of 40, we are looking for all combinations of two whole numbers (a, b) such that: a+b=40anda,b∈W (whole numbers)a + b = 40 \quad \text{and} \quad a, b \in \mathbb{W} \text{ (whole numbers)}

We can approach this by choosing values for a from 0 to 40 and finding the corresponding b:

• If a = 0, then b = 40
• If a = 1, then b = 39
• If a = 2, then b = 38
• …
• If a = 40, then b = 0

So, for each value of a from 0 to 40, there is exactly one corresponding value of b such that a + b = 40.

This gives us: 41 pairs in total41 \text{ pairs in total}

These include both ordered pairs like (0, 40) and (40, 0) — they are considered different unless specified otherwise.

If the question had asked for unordered pairs (meaning (a, b) is the same as (b, a)), we would count only unique combinations without repetition. In that case, we’d count pairs like: (0,40),(1,39),(2,38),…,(20,20)(0, 40), (1, 39), (2, 38), \dots, (20, 20)

That would give 21 unique unordered pairs.

But since the question doesn’t specify ordered or unordered, and asks simply for “how many pairs,” we assume ordered pairs of whole numbers.

✅ Final Answer: 41 pairs of whole numbers have a sum of 40.