<PRE><B>Question 1183595</B>
&lt;br&gt;
Logically, if the sum of two whole numbers is 45, then one of them is even and the other is odd.&lt;br&gt;
If two whole numbers are one even and the other odd, then their difference is an odd number.&lt;br&gt;
Since the problem requires that the difference between the two numbers be less than 10, the difference can be either 1, 3, 5, 7, or 9.&lt;br&gt;
So there are 5 pairs of whole numbers that satisfy the conditions of the problem.&lt;br&gt;
ANSWER: 5&lt;br&gt;
Algebraically....&lt;br&gt;
Let the larger number be x and the smaller be y.&lt;br&gt;
{{{x+y=45}}}
{{{x-y&lt;10}}}&lt;br&gt;
Solve the first equation for y:
{{{y=45-x}}}&lt;br&gt;
Substitute in the inequality:
{{{x-(45-x)&lt;10}}}
{{{2x-45&lt;10}}}
{{{2x&lt;55}}}
{{{x&lt;27.5}}}&lt;br&gt;
The larger number has to be less than 27.5, so the largest it can be is 27.&lt;br&gt;
That&#39;s as far as the algebraic solution gets you; you still have to do some logical reasoning to find the answer to the problem.&lt;br&gt;
Since x is the larger of the two numbers, it has to be greater than 45/2=22.5, so the smallest it can be is 23.&lt;br&gt;
That means the larger number can be any whole number between 23 and 27, inclusive; that is 5 numbers.&lt;br&gt;
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