Soldiers And Their Captains

Algebra Level 1

A group of 1200 people consist only of captains and soldiers. For every 15 soldiers in the group, there is exactly one captain. Find the number of captains in the group.

65 85 80 75

A Former Brilliant Member by A Former Brilliant Member

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6 solutions

Andrew Ellinor
Nov 2, 2015

The most common mistake in this problem is dividing the 1200 people by 15 to determine the number of captains. However, since each squad of captain and soldiers consists of 16 people, it is prudent to perform the division 1200 by 16, indicating the number of squads and thus the number of captains, which is 75.

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thanks for the lesson i learned something new can you show me more i love math

Santiago Rosario - 5 years, 7 months ago
Akshat Sharda
Nov 2, 2015

1200 16 = 75 \frac{1200}{16}=\boxed{75}

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Alakh Saini
Nov 3, 2015

x+15x=1200. 16x=1200. x=1200/16 = 75.

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Farzal Syed
Nov 2, 2015

We can simply think of each garrison (well, I really have less idea about military terms :p ...may b "group" is convenient) consisting 16 members with a captain and 15 soldiers......so the ans is 1200/16 =75 :D

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Trial and error:
Assume there are 75 captains.

So there are 75 "groups".
75 * 15 = 1125 soldiers (EXCLUDING captains)

1200 = no. of soldiers and captains combined

1200 - 1125 = 75 --> this is the number of captains

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Achille 'Gilles'
Nov 2, 2015

? = 1200 / (1 Captain + 15 Soldiers) = 75

So 75 groups captain-soldiers, therefore 75 captains

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