Question 79892: Two ranchers sold a herd of cattle and received as many dollars for each cow as there cattle in the herd. With the money they bought a flock of sheep at $10 per head, and then with the rest of the money they bought a lamb. Later they divided the animals between them, with one rancher obtaining an extra sheep and the other, the lamb. The rancher who got the lamb was given his friend's new pocketknife as compensation. What was the value of the pocketknife?
Answer by Domtone(2)   (Show Source):
You can put this solution on YOUR website! Because the two ranchers sold the cows for as many dollars for each cow as there were in the herd, the amount of dollars they receive is the number of cows squared. So they now have a square number of dollars.
To find the amount of money they have, consider some square numbers.
2x2=4
3x3=9
4x4=16
5x5=25
6x6=36
7x7=49
8x8=64
9x9=81
10x10=100
11x11=121
12x12=144
13x13=169
14x14=196
One of the ranchers gets an extra sheep, so you know they buy an odd number of sheep.
When you divide the amount of money they have before they buy the sheep by $10, you should get an odd number plus some remainder (which will be used to buy the lamb).
36 and 196 are the two numbers listed above that work. If you were to list even more square numbers, you would find that if it gives us an odd number when divided by 10, it also gives us a remainder of 6.
So the lamb cost 6 dollars, and to make up for that the knife must be worth 4 dollars.
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