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Omni-MATH / In a math test, there are easy and hard questions. The easy questions worth 3…

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problem

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.
Plain-text mathematical notation (without MathML)
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 (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.
Original LaTeX notation
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 $\frac{3}{2}$.\\
Knowing that the number of easy questions is 9 times bigger the number of hard questions, find the number of questions in this test.

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Source and history

task_id
245d1395-8d86-5127-9ee1-93032d10914c
task_key
test--245d1395-8d86-5127-9ee1-93032d10914c
task_revision_id
1
config / split
/ test

Official source

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