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OMCPLP 2017 Problem 1

  • Day 1

In a math test, there are easy and hard questions. The easy questions worth 3 points and the hard questions worth D points. If all the questions begin to worth 4 points, the total punctuation of the test increases 16 points. Instead, if we exchange the questions scores, scoring D points for the easy questions and 3 for the hard ones, the total punctuation of the test is multiplied by 32\frac{3}{2} . Knowing that the number of easy questions is 9 times bigger the number of hard questions, find the number of questions in this test.

Dataset text AI-MO AoPS. Quoted with source.

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