sally read 21 pages of a book on Satuday. She read 5/9 of the remainder on Sunday. If she still had 1/3 of the book left to read, how many pages were there in the book?
number of pages ---- x
at end of Saturday, number of pages left = x-21
she read 5/9 of those, leaving 4/9(x-21) pages
but this is supposed to be 1/3 of the pages
4/9(x-21) = (1/3)x
times 9
4(x-21) = 3x
4x - 84 = 3x
x = 84
There were 84 pages in the book
check:
she read 21 pages on Saturday leaving 63
on Sunday she read 5/9 of that or 35 pages
leaving her with 28 pages to read
and 1/3 of 84 = 28
To find the total number of pages in the book, we can work backwards from the given information.
Let's start by finding out the number of pages Sally had left to read after Saturday. If Sally read 21 pages on Saturday and still had 1/3 of the book left, we can determine the fraction she read as 1 - 1/3 = 2/3.
So, 2/3 of the book is equal to 21 pages.
To find 1/3 of the book, which Sally still had left to read, we can divide 21 pages by 2/3.
Dividing by a fraction is the same as multiplying by its reciprocal:
21 pages * (3/2) = 63/2 = 31.5 pages.
Since we cannot have half pages in a book, we round up to the nearest whole number: 32 pages.
Therefore, there were 32 pages in the book.