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Question 646752: If in the army there is one officer for every 16 privates, how many officers are there in a regiment consisting of 1,105 officers and privates?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
Answer by ikleyn(53341)  (Show Source):
You can put this solution on YOUR website! .
If in the army there is one officer for every 16 privates, how many officers are there in a regiment
consisting of 1,105 officers and privates?
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The solution in the post by @Theo is incorrect and goes far out of the target.
I came to bring a correct solution.
I will give two solutions: one arithmetic and other algebraic.
Arithmetic solution
According to the problem we can group all people in groups, each containing 16 privates and 1 officer.
So, each group is 17 people. The number of groups is 1105 divided by 17, which is
 = 65.
So, there 65 groups and, correspondingly, 65 officers.
ANSWER. 65 officers and 1105 - 65 = 1040 privates.
Algebraic solution
Let x be the number of officers. Then the number of privates is 16x, according to the problem.
Write an equation for the total
x + 16x = 1105.
Simplify and find x
17x = 1105, x = 1105/17 = 65.
We get the same answer: 65 officers and 1105 - 65 = 1040 privates.
So, the problem is solved in two ways for your better understanding.
The algebra solution is, actually, the same Arithmetic solution, retold using formulas instead of words.
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