Question

Nora had already read 30% of the book before her teacher assigned it to the class. She is choosing between two options to finish reading the book.
• Option 1: read 25% of the remaining pages each night

• Option 2: read 28 pages each night
Which option should Nora use to finish the book in the least amount of time?
Fill in the blanks to complete the statements.

Nora has already read ____ pages. She has ____ pages remaining in the book. Nora should choose Option ____ because it will take her ____ nights to finish instead of ____ nights with Option ____. ​

Answer 1

Answer:

Let p represent the # of pages in the book.  Then, Nora has already read 0.30p pages and has 0.70p pages left to read.

If she reads 25% pages/night, that means reading 0.25(0.70)p pages per night, or 17.5 pages/night.  If 28% p/n, that means 0.28(0.70)p pages/night, or 19.6p pages/night.

How many nights will it take Nora to finish the book if she reads 25% of 7/10 of the book per night?  Without any calculations, we can answer this by "4 nights, since she reads 1/4 of the unread portion of the book per night."

If she reads 28% of 7/10 of the book per night, that will require fewer nights:

First night:  28%

Second night:  28%  

Third night:  28%

 Total:  3(28%) = 84%

This leaves 16% to read on the final night.

This is one interpretation of what I think is a poorly worded question.

The author of this question might have meant reading 25% of the remaining unread pages per night, which leads to a different answer.