Task 3. (15 points) Lab engineer Dasha received an object for research consisting of about 100 monoliths (a container designed for 100 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 $\frac{1}{7}$. The relative frequency that a randomly selected monolith will be marine clayey loam is $\frac{9}{14}$. How many monoliths of lake-glacial genesis does the object contain, if there are no marine sandy loams among the sandy loams?

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# Solution.

Let's determine the exact number of monoliths. It is known that the probability of a monolith being loamy sand is $\frac{1}{7}$. The number closest to 100 that is divisible by 7 is 98. Therefore, there are 98 monoliths in total. Monoliths of lacustrine-glacial origin consist of all loamy sands ($98: 7=14$) and part of the clay loams. Let's find out how many monoliths of lacustrine-glacial origin are among the clay loams: The total number of clay loams is $98: 7 \cdot 6=84$. Among them, marine clay loams constitute $\frac{9}{14}$ of the total, which is 63. Therefore, the number of clay loams of lacustrine-glacial origin is 21. Thus, the total number of monoliths of lacustrine-glacial origin is: $14+21=35$.

Answer. 35.