Question 1163645
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What do you need help with...?<br>
Make a list of all pairs of whole numbers with a sum of 45 and identify the pairs in which the difference is less than 10.<br><pre>
  44  1
  43  2
  42  3
  41  4
 ...
  30 15
  29 16
  28 17
  27 18
  26 19
  25 20
  24 21
  23 22</pre>
The problem doesn't talk about ORDERED pairs, so I am assuming the pair 22 and 23 is the same as the pair 23 and 22; so you can stop there.<br>
It is easy to see that there are 5 pairs of numbers that satisfy the given condition.<br>
ANSWER: 5 pairs<br>
Here is a solution using logical reasoning and a few simple mental calculations to find the answer, without writing out all those pairs.<br>
(1) The sum of two whole numbers is 45; that means one of them is odd and one is even.
(2) That means the difference between the two numbers is odd.
(3) The difference has to be less than 10; there are 5 positive odd integers less than 10.<br>
ANSWER: 5 pairs<br>