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

Total number of pages is 540.

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.