400 exercise books are arranged into 3 piles.The first has 5 more books than the 2nd pile.The number of books in the second pile is twice the number of books in the third pile.How many books are there in the third pile??

P1 = first pile

P3 = second pile

P3 = third pile

The first has 5 more books than the 2nd pile.

This mean :

P1 = P2 + 5

The number of books in the second pile is twice the number of books in the third pile.

This mean :

P2 = 2 P3

So if :

P2 = 2 P3 and P1 = P2 + 5 then :

P1 = P2 + 5

P1 = 2 P3 + 5

Total number of books = 400

P1 + P2 + P3 = 400

2 P3 + 5 + 2 P3 + P3 = 400

5 P3 + 5 = 400 Subtract 5 to both sides

5 P3 + 5 - 5 = 400 - 5

5 P3 = 395 Divide both sides by 5

5 P3 / 5 = 395 / 5

P3 = 79

P2 = second pile

Paul, if you had looked back, you would have seen that variations of your question have been answered several times

I even did it for you both ways, with 300 books and with 3000 books.

ignore Oscar's reply, I have shown it to be wrong

http://www.jiskha.com/display.cgi?id=1450819688

To solve this problem, we can work backwards using the information given.

Let's denote the number of books in the third pile as "x".

From the information given:
- The first pile has 5 more books than the second pile.
- The number of books in the second pile is twice the number of books in the third pile.

So we can set up two equations using this information:
1) First pile = Second pile + 5
2) Second pile = 2 * Third pile

Now, let's substitute the second equation into the first equation:

First pile = (2 * Third pile) + 5

Since we know that the total number of exercise books is 400, we can set up another equation:

Total number of books = First pile + Second pile + Third pile

400 = (2 * Third pile) + 5 + (2 * Third pile) + Third pile

Simplifying the equation:

400 = 5 + 6 * Third pile

Subtracting 5 from both sides:

395 = 6 * Third pile

Dividing both sides by 6:

Third pile = 395 / 6

Thus, the number of books in the third pile is approximately 65.83. However, since we are dealing with whole numbers (exercise books cannot be divided), we round down to get the final answer:

Therefore, there are 65 exercise books in the third pile.