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

Answer:

160 pages

Explanation:

$Day\ 1 = \frac{1}{4}$

$Day\ 2 = \frac{1}{3}Remainder$

$Left = 80$

Required

The number of pages

Let the number of pages be x.

So, on day 1; we have:

$Day\ 1 = \frac{1}{4}x$

After day 1, there are:$\frac{3}{4}x$ left ----------------- i.e x - 1/4x

On day 2, we have:

$Day\ 2 = \frac{1}{3} * \frac{3}{4}x$

$Day\ 2 = \frac{1}{4}x$

At this point, we have:

$Day\ 1 = \frac{1}{4}x$

$Day\ 2 = \frac{1}{4}x$

$Left = 80$ ---- pages left

The summation of all must equal x, the book pages

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

$\frac{1}{4}x + \frac{1}{4}x+ 80= x$

Simplify the left-hand side

$\frac{1}{2}x+ 80= x$

Collect like terms

$x - \frac{1}{2}x= 80$

Simplify

$\frac{2-1}{2}x= 80$

$\frac{1}{2}x= 80$

Multiply by 2

$2 * \frac{1}{2}x= 80*2$

$x = 160$