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?
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
how do you use long division to solve this question
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.