little help with simple word problems

Hi guys,

I'm a 2nd year university student majoring in Criminology and a minor in Psychology at Simon Fraser University in the Vancouver BC area. that being said; i'm a fail with numbers...

Getting to the point: I have an aptitude test for the Canadian Armed Forces and while reviewing the practice exam I had come across several word problems that I need help fully understanding. I will post them below ( I copied them straight from the practice exam, and the bolded answers is the correct one)


4. 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?
(A) 62 (B) 65 (C) 67 (D) 69

10. How many soldiers are there in a group of 27 sailors and soldiers if there
are four fifths as many sailors as soldiers?
(A) 6 (B) 15 (C) 21 (D) 22


I need help understanding how the answers came to be.

Thanks so much , and if any of you are from the Vancouver BC area we could meet up for a beer ! http://cdn.mathhelpforum.com/images/icons/icon12.png

PS i posted in the algebra section because i'd figured the word problems require simple algebra in order to be solved.

For 16 privates we have 1 officer
for 16x2 privates we have 2 officers
for 16x3 privates we have 3 officers
in general for 16 x n privates n officers and total strength of officers and privates = 16 n + n = 17 n which in this case is given to be 1105 thus n = 1105/17 = 65
hence we have 65 officers

For 10.
let the number of soldiers be x then the number of soldiers = 4/5 x
total soldiers and sailors = x + 4/5 x = 9/5 x which in this case is given to be 27.
now you can solve it further

for the first problem; where did you get 17

for the second problem; where did you get 9/5

First: 16 n + 1 n = 17 n
Second one
x + 4/5 x = (9/5 ) x