1. The grade 8 class was assigned their literature circle assignment - and all of the students are SO happy. On the first day, Ava read half of the book. On the second day, she read three eighths more, and 50 pages remained unread in the book. How many pages are in the book? Show your work for
this problem.
Let x be the total number of pages in the book.
Ava read half of the book on the first day: x/2 pages
On the second day, she read three eighths more: (3/8)x pages
Together, Ava has read x/2 + (3/8)x pages. This is equal to the total number of pages in the book minus the 50 pages remaining: x/2 + (3/8)x = x - 50
To solve for x, first find a common denominator for 2 and 8:
x/2 + (3/8)x = 4x/8 + 3x/8 = (4x + 3x)/8 = 7x/8
Now, the equation becomes: 7x/8 = x - 50
Multiplying both sides by 8 to eliminate the fraction:
7x = 8x - 400
Rearranging the terms:
8x - 7x = 400
x = 400
Therefore, the book has a total of 400 pages.