Task 3. (15 points) An educational center "Young Geologist" received an object for research consisting of about 300 monoliths (a container designed for 300 monoliths, which was almost completely filled). Each monolith has a specific name (sandy loam or clayey loam) and genesis (marine or lake-glacial deposits). The relative frequency (statistical probability) that a randomly selected monolith will be sandy loam is $\frac{1}{8}$. The relative frequency that a randomly selected monolith will be marine clayey loam is $\frac{22}{37}$. How many monoliths of lake-glacial genesis does the object contain, if there are no marine sandy loams among the sandy loams?
# Solution.

Let's determine the exact number of monoliths. It is known that the relative frequency of a monolith being loamy sand is $\frac{1}{8}$. The number closest to 300 that is divisible by $8-296$. Therefore, there are 296 monoliths in total. Monoliths of lacustrine-glacial origin consist of all loamy sands $(296: 8=37)$ and part of the clays. Let's find out how many monoliths of lacustrine-glacial origin are among the clays: The total number of clays is 296:8$\cdot$7=259. Among them, marine clays constitute $\frac{22}{37}$ of the total number, which is 176. Therefore, the number of clays of lacustrine-glacial origin is 83. Thus, the total number of monoliths of lacustrine-glacial origin is: $37+83=120$.

Answer. 120.