Task 3. (15 points) In the educational center "Young Geologist," an object consisting of about 150 monoliths (a container designed for 150 monoliths, which was almost completely filled) was delivered. 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 $\frac{2}{11}$. The relative frequency that a randomly selected monolith will be marine clayey loam is $\frac{7}{13}$. 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 $\frac{2}{11}$. The number closest to 150 that is divisible by 11 is 143. Therefore, there are 143 monoliths in total. Monoliths of lacustrine-glacial origin make up all loamy sands ( $143: 11 \cdot 2=26$ ) and part of the loams. Let's find out how many monoliths of lacustrine-glacial origin are among the loams: The total number of loams is 143:11$\cdot$9=117. Among them, marine loams constitute $\frac{7}{13}$ of the total, which is 77. Therefore, the number of loams of lacustrine-glacial origin is 40. Thus, the total number of monoliths of lacustrine-glacial origin is: $26+40=66$.

Answer. 66.