How many pages has he not read yet?

Question

Peter is reading a 193-page book. He has read three pages more than one fourth of the number of pages he hasn’t yet read. How many pages has he not yet read? Estimate how many days it will take Peter to finish the book if he reads about 8 pages per day.

Answer 1

Hi Lindsey.

 

Let x = the number of pages Peter hasn't read yet

Let 193 - x = the number of pages he has read

 

Then translate the sentence into algebra: 193 - x = .25x + 3 (pages read = 1/4(not read) and 3 more)

And solve for x                                       190     = 1.25x

                                                               152   =  x

 

So he has not read 152 pages.

At 8 pages/day that would be 152/8 or 19 days.

 

Let's check to see if it's correct.

 

152 pages not read. 1/4 of 152 = 38. So he has read 38 + 3 or 41. (3 pages more than 1/4 of pages not read)

152 + 41 = 193, which checks.

 

(We could have made x = "pages read" and 193 - x = "pages not read", only then when we solved for x we would have had "read pages" and the problem asked for "not read". So, in general, it makes the problem less work if you make the variable be what the problem is asking for.)

 

Hope this helps.

 

Sincerely,

Diana