I love to give this problem to students.

pic by kaysareTwo Donkeys are walking down the road loaded down with sacks of potatoes. One looks over at the other and says, "hey, if you give me a sack, I'll have twice as many as you; and if I give you one we'll have the same number. Weird, huh?" The other donkey just says, "Geek" and keeps walking. How many potato sacks does each donkey have?

## 4 comments:

The first donkey has 7 and the other has 5 sacks of potatoes.

If y is the number of sacks on the first donkey and x the second then this is true...

y+1=(x-1)*2

and

y-1=x+1

that reduces to:

y=(2*(x-1))-1

and

y=x+2

We solve for x:

x+2=(2*(x-1))-1

x=(2*(x-1))-3

x=2x-2-3

-x=-2-3

x=5

so, if y=x+2, then y=7

I thought for sure that the second donkey was going to say, "Holy crap! A talking donkey!"

d1 = donkey 1's sack count.

d2 = donkey 2's sack count.

(1) d1+1=2(d2-1)

(2) d1-1=d2+1

(3) d1=d2+2 (from (2))

(4) d2+3=2d2-2 (from (1) and (3))

(5) d2=5 (from 4)

(6) d1=7 (from (3) and (5))

So, one of the donkeys has 7 sacks and the other has 5.

logical deduction and iteration:

Condition 1, implies the two donkeys have an odd number of sacks each.

Condition 2, implies the talker has two more sacks.

So, which two adjacent odd numbers fit the bill?.

3 and 1, no

5 and 3, no

7 and 5, bingo

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