Question

How many pairs of whole numbers have a sum of 40

Answer 1

Let
$x$
and
$y$
represent the pairs of whole numbers that have a sum of 40.

This implies that,

$x + y = 40$

This a single linear equation in two variable. To solve this kind of equation, we make one variable the subject. Say,

$y = 40 - x$

Since,
$x$
is a whole number, the domain of the above function is the set of whole numbers.

In order to get a solution, we choose a value for x and then solve for corresponding value of y.

If
$x = - 1$

$y = 40 - - 1$

This means,

$y = 40 + 1 = 41$

Hence,

$(-1,41)$

is one possible solution.

Since the set of whole numbers we can choose for
$x$
is infinitely many,

$There are infinitely many pairs of whole numbers that can add up to 40$