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Find the number of pairs of positive integers (a,b) such that 2a + 3b = 1000.

 Jul 24, 2020
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There are 166 pairs that begin like this (a, b): (497, 2) , (494, 4) , (491, 6) , (488, 8) , (485, 10) , (482, 12) ....etc.

Notice that as "a" DECREASES by 3, "b" INCREASES by 2. This pattern holds for 166 pairs, the last one being:

a = 2  and  b =332.

 Jul 24, 2020

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