Maria ha acquistato un libro, scontato del 15%, al prezzo di 34 euro. Dopo avere letto 1/4 delle pagine del libro. Legge 2/3 delle pagine rimanenti e a questo punto le restano da leggere 104 pagine. Determina: Il prezzo del libro prima dello sconto
Il numero di pagine complessive del libro
La percentuale che rappresenta il numero di pagine che restano da leggere a Maria rispetto al numero di pagine complessivo.

a) 40 euros

b) 416 pages

c) 25%

Step-by-step explanation:

This question can be translated to:

Maria bought a book, discounted by 15%, at the price of 34 euros. After reading 1/4 of the pages of the book. She reads 2/3 of the remaining pages and at this point, she has 104 pages left to read. Determine:

a)  The price of the book before the discount

b) The total number of pages in the book

c) The percentage that represents the number of pages that Maria has left to read out of the total number of pages.

I will answer in English.

a) If P is the price of the book, with a discount of the 15% the price will be:

P' = P - P*(15%/100%) = P - P*0.15 = P*0.85

and P' = 34 eur

34 eur = P*0.85

34 eur/0.85 = 40 eur = P

The original price was 40 euros.

b) Now suppose that the book has N pages.

First, she reads 1/4 of the pages, then we have:

N - (1/4)*N =  (3/4)*N pages left.

Then she reads (2/3) of the remaining (3/4)*N pages.

Then there are:

(3/4)*N - (2/3)*(3/4)*N = (1/3)*(3/4)*N = (1/4)*N

And we know that at this point, there are 104 pages left, then:

104 = (1/4)*N

104*4 = N = 416

c) The total number of pages is 416, this is the 100%

there are 104 pages left in the book, this will represent X%, and we want to find the value of X.

then:

416 = 100%

104 = X%

Let's take the quotient of those two equations:

(416)/(104) = (100%/X%)

Now let's isolate X%.

X% = (104/416)*100% = 0.25*100% = 25%