The ratio of textbooks to novels to atlases in a certain classroom is 2 to 4 to 3. If there are no other books in the...

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Tue Jan 26, 2021 8:19 am

Veritas Prep

The ratio of textbooks to novels to atlases in a certain classroom is 2 to 4 to 3. If there are no other books in the classroom, and if teacher adds textbooks until novels make up 32% of the books present, which of the following could be the number of atlases in the room?

A. 9
B. 16
C. 34
D. 51
E. 78

OA E

Solution:

Let 2x, 4x and 3x be the number of textbooks, novels and atlases that are in the current collection. Let y be the number of textbooks added to the collection. We can create the equation:

4x / (2x + 4x + 3x + y) = 32/100

4x / (9x + y) = 8/25

100x = 72x + 8y

28x = 8y

7x = 2y

x = 2y/7

Since 2 is not divisible by 7, then y must be divisible by 7 so that x is an integer. Furthermore, we see that x is a multiple of 2, and therefore, 3x, the number of atlases, must be a multiple of 6. Looking at the answer choices, we see that only 78 is a multiple of 6. Therefore, it’s the correct answer.

Answer: E