# 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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For every officer (x) there are 16 privates; So, you will have (x) represent the officers and for each (x), there will be 16 privates. If x is 1, there will be 16 privates, if x is 2, there will be 32, etc.

x + 16x

make the formula equal to 1,105 and solve for x:

x + 16x = 1,105

17x = 1,105

x = 65

There are 16 privates for every officer.

Therefore if there are x officers in the regiment, then the number of privates is 16x. So the total number of officers and privates together it is x+16x = 17x.

But the actual number of officers and privates in the regiment is 1105. So both 17x and 1105 must be same.

So 17x = 1105.

We divide both sides by 17:

Therefore, x= 1105/17 = 65.

x is the number of officers we assumed.

So the number of officers in the regiment is 65.