In order to complete a reading assignment

In order to complete a reading assignment on time, Terry planned to read 90 pages per day. However, she read only 75 pages per day at first, leaving 690 pages to be read during the last 6 days before the assignment was to be completed. How many days in all did Terry have to complete the assignment on time?

3 Explanations

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Pranav Karri

Let D= number of days
Implies, total number of pages= 90*D=90D----1st equation

Terry was left with 6 days for completing 690 pages which means she read 75 pages for (D-6)days (as total number of days = D)

therefore total number of pages= 75(D-6)+690-----2nd equation

Now equate the equations 1 an 2

75(D-6)+690= 90D
D=240/15
D=16
therefore number of days =16

Mar 30, 2017 • Comment

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Maria Chernaya

I read about this alternative approach online (at gmatclub.com) and I think it simplifies the problem. Here is the approach I read. I didn't see any flaws with it but I could be wrong.

Terry ended up reading 75 pages per day, or 15 pages less each day than planned. If Terry actually read 90 pages per day, she would have read 540 pages in the last 6 days (90 *6). Instead she ended up reading 690 pages in the last 6 days, meaning she was 150 pages short of her goal.

So 15 pages less each day for x number of days put her behind 150 pages. Clearly x is 10, so she had 10 + 6 days to complete the assignment.

Oct 25, 2015 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Maria :) Yes, this alternate solution is also valid, providing another way to approach the problem. If we define x as the number of days Terry read 75 pages, we can say that (90-75)x = 690 - 9*60, or the difference between how many pages she planned on reading and how many pages she read for x days is equal to the number of extra pages she had to read during the last 6 days. Simplifying, we get 15x = 150, x = 10. The total number of days is the sum of the number of days she read 75 pages (x) and the 6 days she had left (x+6 = total days): x = 10, x+6 = 10+6 = 16 days.
The major difference between the two solutions is that the video explanation solves for d, the number of days, directly, whereas the solution you propose first solves for the number of days that Terry read 75 pages. That being said, both are definitely valid solutions and it's good that you found a solution that helps you better understand the problem. Thanks for sharing! :D

Nov 9, 2015 • Reply

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Mike McGarry, Magoosh Tutor