if 2015 = 101a + 19b, for positive integers a and b, what is the value of a + b?

2015 = 101a + 19b

First, 2015/101=19.95

So the largest number a could be is 19. 2015-19x101=96, which can not be obtained by 19 multiplying an integer.

Now try a=18, then 2015-18x101=197, which also can not be obtained by 19 multiplying an integer.

Now try a=17, 2015-17x101=298, which also can not be obtained by 19 multiplying an integer.

Now try a=16,2015-16x101=399=19x21, so b=21.

Therefore a=16, b=21, a+b=37

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