<PRE><B>Question 1183754</B>
&lt;br&gt;
Both of the solutions in this thread are deficient.&lt;br&gt;
In one of them, the equation and inequality are shown, and nothing is said about how to solve the pair to get the answer to the problem.  And following their suggestion can get you into trouble if you aren&#39;t careful.&lt;br&gt;
So that response is of little help to the student.&lt;br&gt;
In the other response, the statement that x-y&lt;10 means x is the larger of the two whole numbers, which makes most of the pairs she shows in her response invalid.&lt;br&gt;
So that response ends up with the wrong answer.&lt;br&gt;
The question itself is easily solved informally.&lt;br&gt;
(1) Start with the two whole numbers with a sum of 45 whose difference is as small as possible: 23 and 22.
(2) Then add 1 to one of the numbers and subtract 1 from the other to get another pair; then continue until the difference between the two numbers is greater 10 or greater.  You end up with
(23,22) (24,21) (25,20) (26,19) (27,18)&lt;br&gt;
That&#39;s 5 pairs.&lt;br&gt;
ANSWER: 5 pairs&lt;br&gt;
Note the statement of the problem does not make it clear whether or not the &quot;pairs&quot; are ordered.  If the pairs are ordered, then of course the answer is 10 pairs instead of 5.&lt;br&gt;
A formal solution to the problem might go like this.&lt;br&gt;
Let the two whole numbers be x and 45-x.&lt;br&gt;
The difference between the two numbers is less than 10:&lt;br&gt;
{{{abs((45-x)-x)&lt;10}}}
{{{abs(45-2x)&lt;10}}}
{{{-10&lt;45-2x}}} and {{{45-2x&lt;10}}}
{{{2x&lt;55}}} and {{{ 2x&gt;35}}}
{{{x&lt;27.5}}} and {{{x&gt;17.5}}}&lt;br&gt;
Given that the two numbers are whole numbers, the solution set is {{{18&lt;=x&lt;=27}}}&lt;br&gt;
That gives 10 (ordered) pairs, or 5 different unordered pairs.&lt;br&gt;
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