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,


`<b>There are infinitely many pairs of whole numbers that can add up to 40</b>`