Will the Bayou Rise or Fall?

This is a classic problem. Perhaps you have heard it before. I don't remember where I got it. You might want to try to work it before you read my solution. Anyway, Pierre and Budreaux were sitting in a boat on the bayou when Pierre suggested thowing the anchor overboard. Budreaux said that if Pierre did that the anchor would take up space at the bottom of the bayou, causing the level of the bayou to rise a bit. But Budreaux said, on the other hand, without the anchor the boat would float higher, so maybe the level would go down. Pierre replied that maybe these two opposing things would cancel each other out. What is the right answer? Will the level of the bayou rise or fall when the anchor is thrown overboard?

Archimedes said that a floating object will displace a volume of water equal to the weight of the object.

The density of water is 62.4 lb/cf
Assume that a boat and its contents including an anchor weigh 1,000 lb
Then the amount of water displaced is 1,000 lb divided by 62.4 lb/cf = 16.03 cf
Assume the anchor weighs 50 lb
Then the anchor accounts for 50 lb divided by 62.4 lb/cf = 0.80 cf
of the volume of water displaced by the boat and its contents including the anchor.
Assume the anchor is made of cast iron, having a specific gravity of 7.03
Then the density of the anchor is 7.03 * 62.4 lb/cf = 438.67 lb/cf
And the volume of the anchor is 50 lb divided by 438.67 lb/cf = 0.114 cf

A sunken object displaces a volume of water equal to the volume of the sunken object.

When the anchor is thrown overboard it sinks, & the volume of water it displaces is 0.114 cf
Without the anchor, the boat and its contents weigh 1,000 lb - 50.0 lb
= 950.0 lb
Now the amount of water displaced by the boat and its contents is 950.0 lb divided by 62.4 lb/cf
= 15.22 cf
Thus, the total volume of water displaced by the sunken anchor, plus the boat and its contents
absent the anchor, is 0.114 cf + 15.22 cf = 15.34 cf
Since the volume of water displaced by the boat and its contents including the anchor is
16.03 cf, when the anchor is thrown overboard the total amount of water displaced
decreases by 16.03 cf - 15.34 cf = 0.69 cf
causing the level of the lake to fall.
This actually should have been apparent ever since we noted that when the
anchor is in the boat it accounts for 0.80 cf of water displacement, whereas when the anchor is
sunken it displaces only 0.114 cf. Note that 0.80 cf - 0.114 cf
= 0.69 cf, which is the same answer we got above,thus checking my answer.