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# A small library has a maximum capacity of 15,000 books. When the shelves were full, the librarian removed old books to make space for the new ones. In January ${{1}^{st}}$, the library had 13,500 books. Each month they receive an additional 95 books. If y represents the time, in months after January, which of the following inequalities describe the set of months where the library is at or above capacity?

Last updated date: 20th Jul 2024
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Hint: For solving this question you should know about the general mathematical equations and how to make these for the given statements. If we see our problem then it can be solved very easily by just making different – different equations for different conditions. And then merge them with each other at last for finding the actual condition according to our question.

Complete step by step answer:
According to our question, a small library has a maximum capacity of 15,000 books. When the shelves were full, the librarian removed old books to make space for the new ones. In January ${{1}^{st}}$, the library had 13,500 books. If y represents the time, in months after January, which of the following inequalities describes the set of months where the library is at or above capacity?
If we make our equations for solving this question then, total capacity of library $=15,000$books
And on January ${{1}^{st}}$ have books in library $=13,500$
In each month the new books comes are 95,
For y time $=95\times y=95y$
So, total books in library in y – time $=13500+95y$
Hence,
\begin{align} & 13500+95y\le 15000 \\ & 95y\le 15000-13500 \\ \end{align}
So, the correct equation for this is,
$95y\le 15000-13500$
$95y\le 1500$
$19y\le 300$

Note: While solving this type of questions you should know about how to make the equation from the given condition statements. And be careful when making an equation and assure that it must be satisfying to the sentence.