Question

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

Answer 1

• Jim's: 7
• Duke's: 21
• Hank's: 11

Explanation:

Let J, D, and H represent the drove sizes of Jim, Duke, and Hank.

2(H -6 + 1) = (J +6 -1) . . . . . Hank's offer

3(D -14 +1) = (H +14 -1) . . . . Duke's offer

6(J -4 +1) = (D +4 -1) . . . . . . Jim's offer

These equations can be simplified to ...

2H - J = 15

3D - H = 52

6J - D = 21

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Solution

Adding twice the second equation to the first gives ...

2(3D -H) +(2H -J) = 2(52) +(15)

6D -J = 119

Adding 6 times the third equation to this one gives ...

6(6J -D) +(6D -J) = 6(21) +(119)

35J = 245

J = 7

Using this value in the third equation gives ...

6(7) -D = 21

42 -21 = D = 21

Using the value of J in the first equation gives ...

2H -7 = 15

H = (15 +7)/2 = 11

Then the solution is (J, D, H) = (7, 21, 11).

Jim's drove had 7 animals; Duke's drove had 21 animals; Hank's drove had 11 animals.