Question

A bookshelf holds both paperback and hardcover books. The ratio of paper-back books to hardcover books is 22 to 3. How many paperback books are on the shelf? The number of books on the shelf is between 202 and 247, inclusive
$(a){\text{ 205}}$
$(b){\text{ 2305}}$
$(c){\text{ 225}}$
$(d){\text{ 198}}$

Answer 1

Hint: In the above given question, assume the number of paperback books and hardcover books according to the ratio given. Then, find the multiple of the coefficient of the total number of books by using the other given conditions.

Complete step-by-step solution -
It is given in the question the ratio of paperback books to hardcover books is 22 to 3.
Let the number of paperback and hardcover books be \[22x\;\] and \[3x\] respectively.
So, the total number of books \[ = 22x + 3x\]
\[ = 25x\]
So, \[25x\] lies between 202 and 247
So, the multiple of 25 in between 202 and 247 is 225.
So, we get,
\[25x = 225\;\;\]
$ \Rightarrow \;x = 9$
As we have assumed the number of paperback books \[ = \;22x\]
After substituting the value of $x$, we get
\[ = 22 \times 9\]
\[ = 198\]
Therefore, there are 198 paperback books on the shelf.
Hence, the correct answer is the option $(d)$.

Note: For this question, assume the number of paperback covers to be \[22x\;\] and the number of hardcover books to be \[3x\]. Then, using these constraints and the other given conditions in the question, you will obtain the required solution.