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?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~



        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.


<pre>
                <B><U>Arithmetic solution</U></B>


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

    {{{1105/17}}} = 65.


So, there 65 groups and, correspondingly, 65 officers.


<U>ANSWER</U>.  65 officers and  1105 - 65 = 1040 privates.


                <B><U>Algebraic solution</U></B>


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.
</pre>

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.