Respuesta :
Answer:
There are 28 fruits in each pile.
Step-by-step explanation:
We are given the following in the question:
Let x denote the number of fruits in each pile and y denote the number of fruits that every traveler receive.
Consider the diophantine equation:
[tex]63x + 7 = 23y\\63x-23y = -7[/tex]
We obtain the greatest common divisor of (63,-23).
The greatest common divisor f 63 and -23 is 1.
Therefore, there exist [tex]\alpha,\beta[/tex] such that
[tex]-23\alpha+63\beta=1[/tex]
By applying extended Euclidean Algorithm, we have,
[tex]1 = (1\times 6)+(-1\times 5)\\1 = (1\times 17)+(3\times 6)\\1 = (3\times 23)+(-4\times 17)\\1 = (-4\times 40)+(7\times 23)\\1 = (7\times 63)+(-11\times 40)\\1 = (-11\times -23)+(-4\times 63)[/tex]
[tex]1 = (-11\times -23) + (-4\times 63)[/tex]
Multiplying -7 on both sides, we get,
[tex]-7 = (77\times -23) + 28\times 63)[/tex]
Thus, we get,
[tex]x = 28\\y=77[/tex]
Thus, there are 28 fruits in each pile.
