SOLUTION: Last year there were 105 students divided evenly into a number of sections. This year, there are 175 students, and to maintain the same ratio of students to sections, 2 additional

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Last year there were 105 students divided evenly into a number of sections. This year, there are 175 students, and to maintain the same ratio of students to sections, 2 additional      Log On


   

Question 1170887: Last year there were 105 students divided evenly into a number of sections. This year,
there are 175 students, and to maintain the same ratio of students to sections, 2 additional sections
are added. How many sections were there last year?
Answer by ikleyn(52943) About Me  (Show Source):
You can put this solution on YOUR website!
.

Wording is very poor in this post,


but, straining my guessing skills, I can imagine


     +--------------------------------------------------------------------+
     |    that were there n groups last year with x students in each,     |
     |        with  nx = 105,                                             |
     |    and that there are (n+2) groups this year with the same number  | 
     |    x of students in each group, with  (n+2)*x = 175.               |
     +--------------------------------------------------------------------+


If so, then I have two equation


     nx = 105         (1)
and
     (n+2)x = 175.    (2)


Subtracting equation (1) from equation (2), I get

    2x = 175 - 105 = 70;  hence  x = 70/2 = 35


and the number of groups last year was  n= 105/35 = 3.    ANSWER

Solved.