Question

How many pairs of whole numbers have sum of 110

Answer 1

Because the number is even, then the number of possible combinations will be: 110/2 = 55 let's consider a simpler example, the number: 10, then we have: 10+0, 9+1, 8+2, 7+3, 6+4, which is equal to 10/2 =5 combinations. Note: We are not considering permutations between the elements of the sum therefore 10+0, 0+10 counts as one combination.

Answer 2

Solution: The are total 56 pairs of whole numbers whose sum is 110.

Explanation:

The whole numbers are all positive integers including 0.

If the sum is an even number n then the pairs of whole numbers are $\frac{n}{2} +1$.

If the sum is an odd number n then the pairs of whole numbers are $\frac{n+1}{2}$.

Since 110 is an even number therefore the pairs of whole number with sum 10 are

$\frac{110}{2} +1=55+1=56$

And the pairs are (0,110),(1,109),...,(55,55) after that the pairs are repeated so we can't  consider those repeated pairs.

For example we have to find the pairs of whole numbers have sum of 6. So the pairs are (0,6),(1,5),(2,4),(3,3) and from the formula the number of pairs is $\frac{6}{2} +1=3+1=4$.

Hence, the are total 56 pairs of whole numbers whose sum is 110.