How many pairs of whole numbers have a sum of 40?

A whole number is one of the numbers set {0, 1, 2, 3, 4, ...}. They are a set of positive integers along with zero and don't include the fraction or decimal numbers.

We determine how many pairs of whole numbers have a sum of 40. Let us notice below.

(0, 40)
(1, 39)
(2, 38)
(3, 37)
(4, 36)
(5, 35)
(6, 34)
(7, 33)
(8, 32)
(9, 31)
(10, 30)
(11, 29)
(12, 28)
(13, 27)
(14, 26)
(15, 25)
(16, 24)
(17, 23)
(18, 22)
(19, 21)
(20, 20)

Hence, there are 21 pairs.

The next setting is a repeat pair. Remember, because the order in pairs does not have an effect so that $\boxed{ \ (a, b) \ is \ equal \ to \ (b, a) \ }$, vice versa. Exactly like this:

(21, 19) ⇔ (19, 21), (22, 18) ⇔ (18, 22)

and so forth, until (39, 1) ⇔ (1, 39), (40, 0) ⇔ (0, 40)

Note, we can use the principle of finding many terms from the arithmetic sequence, even though they are not too many.

The general term of an arithmetic sequence (aₙ) with common difference d is $\boxed{ \ a_n = a_1 + (n - 1)d \ }$

Given:

The first term a₁ = 0
The common difference d = 1 (from 1 - 0, 2 - 1, etc.)
The last term aₙ = 20

How many terms (n)?

$\boxed{ \ a_n = a_1 + (n - 1)d \ }$

$\boxed{ \ 20 = 0 + (n - 1) \cdot 1 \ }$

$\boxed{ \ 20 = n - 1 \ }$

$\boxed{ \ 20 + 1 = n \ }$

We get $\boxed{ \ n = 21 \ }$, i.e., whole numbers pairs that have a number of 40.

A complete description of natural numbers, whole numbers, and integers can be explored at https://brainly.com/question/1852063.

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Keywords: whole numbers, how many pairs, a sum of 40, exact, positive numbers, integers, natural, arithmetic sequence