Question

If Mark reads 18 pages less per day than originally planned, he will need 5 extra days to finish the book. If he reads 24 pages less per day, he will need 8 extra days to finish. How many pages does the book have?
PLZ HELP

Answer 1

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.

$(x-18)(d+5)=xd$

$xd+5x-18d-90=xd$

$5x-18d=90$            .... (1)

He reads 24 pages less per day, he will need 8 extra days to finish.

$(x-24)(d+8)=xd$

$xd+8x-24d-192=xd$

$8x-24d=192$

$x-3d=24$       ... (2)

Subtract 5 times of equation (2) from equation (1).

$5x-18d-5(x-3d)=90-5(24)$

$5x-18d-5x+15d=90-120$

$-3d=-30$

$d=10$

Substitute d=10 in equation (1).

$5x-18(10)=90$  

$5x-180=90$  

$5x=90+180$

$5x=270$

Divide both sides by 5.

$x=54$

Total number of pages

$xd=(54)(10)=540$

Therefore , the total number of pages is 540.