SOLUTION: Two long books containing a total of 2400 pages have a ratio of 3 pages to 5 pages. How many pages are in each book?

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Question 220999: Two long books containing a total of 2400 pages have a ratio of 3 pages to 5 pages. How many pages are in each book?

Answer by drj(1380) About Me  (Show Source):
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Two long books containing a total of 2400 pages have a ratio of 3 pages to 5 pages. How many pages are in each book?

Step 1. Let x be the number of pages of the first book.

Step 2. Let 2400-x be the number of pages of the second book.

Step 3. 3%2F5=x%2F%282400-x%29 since the two long books containing a total of 2400 pages have a ratio of 3 pages to 5 pages.

Step 4. Multiplying 5(2400-x) to both sides of the equation in Step 3 to get rid of the denominators yields

5%2A%282400-x%29%2A3%2F5=5%2A%282400-x%29%2Ax%2F%282400-x%29

3%2A%282400-x%29=5x

7200-3x=5x

Adding 3x to both sides yields

7200-3x%2B3x=5x%2B3x

7200=8x

Divide by 8 to both sides of equation

7200%2F8=8x%2F8

x=900 then 2400-x=1500 and 900/1500=3/5.

Step 5. ANSWER: One book has 900 pages and the other book has 1500 pages.

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J