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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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You are given a system, consisting of one equation and one inequality
x + y = 45 (1)
x - y < 10 (2)
Let solve the problem graphically to make the solution visible.
The figure below shows the line x + y = 45 (red line) and line y = x - 10 (green line).
The solution set for the system (1), (2) is the set of integer points on the red line, that are ABOVE the green line.
Plot x + y = 45 (red), y = x -10 (green)
You can calculate these points manually.
Their number is (a) 28, if the zero is admitted for x as a whole number,
or (b) 27, if the zero is NOT admitted for x as a whole number.
The set of solutions is (0,45), (1,44), (2,43), (3,42), . . . , (27,18) in case (a) (28 pairs)
or (1,44), (2,43), (3,42), . . . , (27,18) in case (b) (27 pairs)
