Question

the first day anna read a quarter of the book. on the second day she read a third of the remainder. noticed that after two days he had 80 pages left unread. how many pages did the book have?​

Answer 1

160 pages

Step-by-step explanation:

`Day\ 1 = (1)/(4)`

`Day\ 2 = (1)/(3)Remainder`

`Left = 80`

Required

The number of pages

Let the number of pages be x.

So, on day 1; we have:

`Day\ 1 = (1)/(4)x`

After day 1, there are:
`(3)/(4)x` left ----------------- i.e x - 1/4x

On day 2, we have:

`Day\ 2 = (1)/(3) * (3)/(4)x`

`Day\ 2 = (1)/(4)x`

At this point, we have:

`Day\ 1 = (1)/(4)x`

`Day\ 2 = (1)/(4)x`

`Left = 80` ---- pages left

The summation of all must equal x, the book pages

`Day\ 1 + Day\ 2 + Left = Total\\`

`(1)/(4)x + (1)/(4)x+ 80= x`

Simplify the left-hand side

`(1)/(2)x+ 80= x`

Collect like terms

`x - (1)/(2)x= 80`

Simplify

`(2-1)/(2)x= 80`

`(1)/(2)x= 80`

Multiply by 2

`2 * (1)/(2)x= 80*2`

`x = 160`