Andreas received a new book for his birthday. He read 3/8 of the book in the first week, then 53 more pages in the second week. If he still has 117 pages to read, how many total pages are in his book?

Question

Andreas received a new book for his birthday. He read 3/8  of the book in the first week, then 53 more pages in the second week. If he still has 117  pages to read, how many total pages are in his book?

anonymous · Answer

Let the total number of pages in the book be: x

-In the first week, he reads 3/8 of the book, so in the first week he reads (3/8)*x pages
-In the second week, he reads 53 pages.
-After all this, he has 117 pages left

So basically you can divide the book in to three sections, first week, second week and pages left after second week. All these when added equal the total number of pages in the book.

So by this relation, you can draw the following equation:

$$(3x \div8) + 53 + 117 = x$$

Separate variable and non-variable terms, you get:
$$53 + 117 = x - (3x \div8)$$

 => $$170 = (8x - 3x) \div8$$
 => $$170*8 = 5x$$
=> $$1360 = 5x$$

Now solve for x, this gives you, x= 272
The book has 272 pages