The SimCity navy has a rigorous training program

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Discussion Overview

The discussion revolves around a mathematical problem posed by a scenario involving cadets in a naval training program who must fight sharks. Participants analyze the relationships between the number of cadets, sharks, and their respective legs and heads, aiming to determine how many sharks were killed. The focus is on mathematical reasoning and problem-solving.

Discussion Character

  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One cadet notes that there were 4 times as many cadets in the water as there were sharks, leading to the equation c = 4s.
  • Another cadet states that the total number of legs is equal to the square of the number of sharks, represented as L = s^2.
  • A third cadet claims that the number of cadet legs is 14 more than the total number of cadet and shark heads, expressed as L = 14 + c + s.
  • By substituting the previous equations, participants derive the quadratic equation s^2 - 5s - 14 = 0.
  • One participant concludes that the positive solution to the equation is s = 7, suggesting that 7 sharks were killed.
  • Another participant mentions that there were 28 cadets, but notes they had only 49 legs, indicating a discrepancy or error in the earlier calculations.
  • Some participants express frustration or humor regarding the timing of their responses and the accuracy of their contributions.

Areas of Agreement / Disagreement

There is no clear consensus on the final answer, as some participants present conflicting information regarding the number of cadets and their legs, and the discussion includes humor and corrections without resolving the discrepancies.

Contextual Notes

The discussion includes assumptions about the number of legs per cadet and the implications of the mathematical relationships presented. There are unresolved aspects regarding the total number of cadets and the accuracy of the calculations.

Greg Bernhardt
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The SimCity navy has a rigorous training program. In order to graduate from the naval academy, cadets must enter a pool and fight sharks. Today, a group of cadets was tested. Each cadet put on his mask, snorkel, and two flippers; and armed himself with a knife. Then the cadets jumped into the pool. The sharks were then released from their pens. After 10 minutes of gruelling hand-to-fin combat, all of the sharks were killed. Miraculously, none of the cadets were killed. Exiting the pool, the cadets began to haul the shark bodies out of the water. The dead sharks were soon lying in a row. One of the cadets noted that during the fight, there were 4 times as many cadets in the water as there were sharks. A second cadet then stated that the number of legs they now had was equal to the square of the number of sharks. A third said that the number of cadet legs was 14 more than the total number of cadet and shark heads. How many sharks were killed?
 
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Greg Bernhardt said:
One of the cadets noted that during the fight, there were 4 times as many cadets in the water as there were sharks.

c = 4s

A second cadet then stated that the number of legs they now had was equal to the square of the number of sharks.

L = s^2

A third said that the number of cadet legs was 14 more than the total number of cadet and shark heads. How many sharks were killed?

L = 14 + c + s

By substitution,

s^2 = 14 + 4s + s

Rearranging,

s^2 - 5s - 14 = 0

(s-7) (s+2) = 0

Rejecting the negative solution, s = 7.
 
28 cadets, though with only 49 legs amongst them.

Njorl
 
D'oh!

Not only was I not quick enough, I answered with the wrong 2 quantities.

Njorl
 
Seven? :smile:

Too late.
 
looks like someone knew the answer without reading the question.. hmmhm? :rolleyes:
 

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