Question

Гонорар за книгу был распределён между тремя авторами в отношении 8:6:5. Если бы этот гонорар был распределён как 7:5:4, то один из соавторов получил бы на 2500 рублей больше, чем он получил на самом деле. Чему равна сумма гонорара?

Answer 1

Пошаговое объяснение:

8х+6х+5х=7у+5у+4у

19х=16у

Х=16у/19

Первый получил на 2500 руб больше

7у-8х=2500

-8х=2500-7у

8х=7у-2500

Х=(7у-2500) /8

16у/19=(7у-2500)/8

16у×8=19(7у-2500)

128у=133у-47500

5у=47500

У=9500

Х=16×9500/19=8000

8×8000=64000 руб - первый

6×8000=48000 руб - второй

5×8000=40000 руб - третий

Второй получил на 2500 руб больше

5у-6х=2500

6х=5у-2500

Х=(5у-2500)/6

16у/19=(5у-2500)/6

19(5у-2500)=16у×6

95у-47500=96у

95у-96у=47500

-у=47500

У= - 47500 - не подходит

Третий получил на 2500 руб больше

4у-5х=2500

5х=4у-2500

Х=(4у-2500)/5

16у/19=(4у-2500)/5

19(4у-2500)=16у×5

76у-47500=80у

76у-80у=47500

-4у=47500

У= - 11875 - не подходит

Сумма гонорара =64000+48000+40000=

=152000 рублей

Ответ : 152000 рублей

Answer 2

Calculation of Royalty Distribution

To find the total amount of the royalty, we need to solve the given system of equations. Let's assume the total royalty amount as 'x'.

According to the given information, the distribution of the royalty between the three authors is in the ratio of 8:6:5. This means that the first author receives 8 parts, the second author receives 6 parts, and the third author receives 5 parts.

If the royalty was distributed in the ratio of 7:5:4, then the first author would receive 7 parts, the second author would receive 5 parts, and the third author would receive 4 parts.

We are also given that if the distribution was in the ratio of 7:5:4, one of the co-authors would receive 2500 rubles more than they actually received.

Let's solve this system of equations to find the total amount of the royalty.

Equations:

1. 8x - 7x = 2500 2. 6x - 5x = 0 3. 5x - 4x = 0

Solution:

Simplifying the equations, we get:

1. x = 2500 2. x = 0 3. x = 0

Since the second and third equations have no solution, we can conclude that the total amount of the royalty is 2500 rubles.

Therefore, the sum of the royalty is 2500 rubles.