Answer to July 2016 Problem of the Month

Three Texas drovers met on a highway and began to dicker as follows:
Hank says to Jim: "I'll give you six pigs for a hoss; then you'll have twice
as many critters in your drove as I will have in mine."

Duke says to Hank: I'll give you fourteen sheep for a hoss; then you'll have
three times as many critters as I."

Jim says to Duke: I'll give you four cows for a hoss; then you'll have six
times as many critters as I."

From these interesting facts, can you tell how many animals were in each
of the three droves?

Solution to the Problem:

Hank had 11 animals, Jim 7, and Duke 21, making a total of 39 animals altogether.

Let x = number of critters that Hank had.
Let y = number of critters that Jim had.
Let z = number of critters that Duke had.

Then write three equations from the three statements above:
(1) Hank to Jim: 2(x - 5) = y + 5
(2) Duke to Hank: x + 13 = 3(z - 13)
(3) Jim to Duke: z + 3 = 6(y - 3)

Solving:
(1) 2x - 10 = y + 5
(2) x + 13 = 3z - 39
(3) z + 3 = 6y - 18

(1) 2x - y = 15
(2) x - 3z = -52
(3) -6y + z = - 21

Now solve the 3 equations with 3 unkowns to get x = 11, y = 7, and z = 21.

Correctly solved by:

1. James Alarie	Flint, Michigan
2. Yaniv M. Maman	Houston, Texas