Question 221000
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.  {{{3/5=x/(2400-x)}}} 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*(2400-x)*3/5=5*(2400-x)*x/(2400-x)}}} 


{{{3*(2400-x)=5x|||


{{{7200-3x=5x}}}


Adding 3x to both sides yields


{{{7200-3x+3x=5x+3x|||


{{{7200=8x}}}}


Divide by 8 to both sides of equation


{{{7200/8=8x/8}}}


{{{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