Tyler reads 2/15 of a book on Monday, 1/3 of it on Tuesday, 2/9 of it on Wednesday, and 3/4 of the remainder on Thursday. If he still has 14 pages left to read on Friday, how many pages are there in the book?
Answers
Answer:
Let x be the number of pages in the book.
On Monday, he reads 2/15x. On Tuesday, he reads 1/3x. On Wednesday, he reads 2/9x. To add these, we need a common denominator; 45 is the least common denominator.
Converting these we have 6/45x, 15/45x and 10/45x. These combine to make:
(6/45x+15/45x+10/45x) = 31/45x
On Thursday, he reads 3/4 of the remainder of the book. He has (1-31/45)x left; this is 14/45x. He reads 3/4 of this; this is 3/4(14/45) = 42/180x.
This means so far he has read 31/45x+42/180x. 180 would be a common denominator; converting these fractions we have
124/180x+42/180x = 166/180x
At this point, he has 14 pages left; this means he has read 14 pages less than x, the total number of pages. This gives us the equation
166/180x = x-14
Subtracting 166/180x from each side, we have
0 = 14/180x - 14
Adding 14 to each side gives us
14 = 14/180x
Dividing both sides by 14/180, we have
14(180)/14 = x
180 = x
hope it helps
Answer:180
Step-by-step explanation: