Question 1143565
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The sum of two whole number is 45 and their difference is less than 10. The number of all possible {{{highlight(cross(pair))}}} <U>pairs</U> 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).


<U>Answer</U>.  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.
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