Answer:
Total number of pages is 540.
Step-by-step explanation:
Let mark read x be he number of pages per day and d be the number of days to finish the book.
Total number of pages = xd
Mark reads 18 pages less per day than originally planned, he will need 5 extra days to finish the book.
[tex](x-18)(d+5)=xd[/tex]
[tex]xd+5x-18d-90=xd[/tex]
[tex]5x-18d=90[/tex] .... (1)
He reads 24 pages less per day, he will need 8 extra days to finish.
[tex](x-24)(d+8)=xd[/tex]
[tex]xd+8x-24d-192=xd[/tex]
[tex]8x-24d=192[/tex]
[tex]x-3d=24[/tex] ... (2)
Subtract 5 times of equation (2) from equation (1).
[tex]5x-18d-5(x-3d)=90-5(24)[/tex]
[tex]5x-18d-5x+15d=90-120[/tex]
[tex]-3d=-30[/tex]
[tex]d=10[/tex]
Substitute d=10 in equation (1).
[tex]5x-18(10)=90[/tex]
[tex]5x-180=90[/tex]
[tex]5x=90+180[/tex]
[tex]5x=270[/tex]
Divide both sides by 5.
[tex]x=54[/tex]
Total number of pages
[tex]xd=(54)(10)=540[/tex]
Therefore , the total number of pages is 540.
