# The cost of an angry ox A.  According to the simple meaning of the verse, if one person’s ox kills another’s then you shall sell the killer ox and the carcass of the dead ox. Then you split the proceeds from both between the two owners [Shemos (Exodus) 21:35]. Write a formula to show how much money each owner would get from the sale using the following variables:

D = sale price of dead ox
L = sale price of killer ox
\$ = amount received by each
(D+L) / 2 = \$

B.  The Gemara explains that it is not necessary to actually sell the animals, but that we use this formula to determine how much the owner of the killer ox would have to pay to the owner of the dead ox [Bava Kamma 34a]. However, Rashi points out that there is a problem with reading this literally; it could result in a profit for the owner of the killer ox. What if the value of the killer ox was only \$100 and the dead ox was worth \$1,000. Using the formula from the prior question how much would each of the owners get?
(\$100 + \$1000)/ 2 = \$550

C. How much profit would the owner of the killer ox be making?
\$550 – \$100 = \$450 profit

D. How much would the owner of the dead ox be losing?
\$1000 – \$550 = \$450 loss

E.  It is clearly unfair that the owner of the killer ox would make a profit.  Rashi resolves this issue by explaining that the statement in Shemos is refering to a case where the oxen are of the same value. This way the owner of the killer ox would never make a profit.
Rashi addresses how to determine the law in cases where the oxen were of different values. He says that to figure out what the owner of the dead ox is entitled to, take the difference between the value of the ox when it was living and the value of its carcass. Then take half of that amount and add it to the value of the carcass. Write a formula for this.

D = value of the carcass of the dead ox
L = value of the ox (now dead) when it was living
\$ = amount of restitution owed to the owner of the dead ox.
D + (L-D)/ 2  = \$

F.  You now have two formulas:
The literal reading of the Chumash to be used when the oxen are of the same value: (D+L) / 2 = \$
Rashi’s interpretation to be used when the oxen are of different values:  D + (L-D)/ 2 = \$
Show that the first formula is equal to the second formula.
(D+L) / 2 = D + (L-D)/ 2
2 * [(D+L) / 2] = 2 * [D + (L-D)/ 2]
D + L = 2D + (L – D)
D + L = D + D + L – D
D + L = D + L

G. There are situations where the owner of the dead ox will not get full compensation. In that case the owner of the dead ox will only get as much as they out of the combined sale of the sale of the killer ox and the carcass if the dead ox.  If a killer ox (worth \$150) kills an ox worth \$1,200 and the value of the carcass is only worth \$50, how much will the owner of the dead ox get?
D + (L-D)/ 2 = \$
\$50 + (\$1,200 – \$50) / 2 = \$
\$50 + \$1,150/ 2 = \$
\$50 + \$575 = \$
\$625 = \$

H.  If the carcass were worth \$900 how much would he get?
D + (L-D)/ 2 = \$
\$900 + (\$1,200 – \$900) / 2 = \$
\$900 + \$150 = \$
\$1,050 = \$

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