SOLUTION: The sum of two whole number is 45 and their difference is less than 10. The number of all possible pair is

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Question 1143565: The sum of two whole number is 45 and their difference is less than 10. The number of all possible pair is
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
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The sum of two whole number is 45 and their difference is less than 10. The number of all possible pairs is
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x + y = 45,   (1)
x - y < 10.   (2)   (where x is the larger number)


Express x from (1): x = 45 - y,  and substitute it into (2). You will get


45 - y - y < 10,  or

45 - 2y < 10,  or

2y > 45 - 10,  or

y > (45 - 10)/2.


Hence, y > 17. Then x < 10 + 17 = 27. (And  x > y).


Answer.  These 5 pairs         (27,18), (26,19), (25,20), (24,21), (23,22) 
         and 5 reversed pairs  (18,27), (19,26), (20,25), (21,24), (22,23)  is the full list of solutions.


         In all, there are 10 different pairs of solutions, listed above.


Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


45 divided into the sum of two whole numbers as close to equally as possible gives the pair (22,23). The difference between those two whole numbers is 1.

You can find other pairs by subtracting 1 from the first number in the pair and adding 1 to the second.

Each time you do that, the difference between the two numbers in the pair increases by 2.

Since the difference between the two whole numbers has to be less than 10, you can do that 4 times -- making the difference between the two whole numbers in the pair 1+4(2) = 9.

That gives you the pairs (22,23), (21,24), (20,25), (19,26), and (18,27).

That's a total of 5 pairs.

It's not clear whether you are to look for ordered pairs or just pairs. If you are looking for ordered pairs, then each of the 5 pairs shown can be switched, giving you a total of 10 pairs.

So the answer is either 5 pairs or 10 ordered pairs....
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