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| Math Central | Quandaries & Queries |
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Question from jerry, a parent: the 1st of 4 books has twice as many pages as the 3rd. The 2nd book has 30 pages less than the 1st. The 4th has 42 pages more than the 1st and 2nd books combined. there are 567 pages in total. How many pages are in each book? please show me the answer and how you came to the answer. |
Hi Jerry,
Read the first three sentences in the problem carefully. The first sentence says that if you know the number of pages in book 3 you can tell the number of pages in book 1. The second sentence says that once you know the number of pages in book 1 you can tell the number of pages in book 2. The third sentence says that if you know the number of pages in books 1 and 2 you can tell the number of pages in book 4. Hence the number of pages in book 3 is the key, if you know it you can calculate the number of pages in each book.
Since the number of pages in book three is the key I am going to let it be the variable I use in my solution.
Let the number of pages in book 3 be n.
From the first sentence the number of pages in book 1 is 2n.
How many pages are in book 2?
How many pages are in book 4?
Add the number of pages in the four books. This must be 567. Solve for n.
I hope this helps,
Penny
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