SOLUTION: At a certain school, the number of children entering kindergarten increased by 6.7% annually for 5 years, then decreased by 4.2% annually in the next 5 yesrs. If 110 children enrol

Algebra ->  Percentages: Solvers, Trainers, Word Problems and pie charts -> SOLUTION: At a certain school, the number of children entering kindergarten increased by 6.7% annually for 5 years, then decreased by 4.2% annually in the next 5 yesrs. If 110 children enrol      Log On


   

Question 609189: At a certain school, the number of children entering kindergarten increased by 6.7% annually for 5 years, then decreased by 4.2% annually in the next 5 yesrs. If 110 children enrolled in kindergarten at the beginning of this period, how many were enrolled after 10 years?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Your problem describes a sequence of percent changes. I find that a simple way to solve these kinds of problems is to use the following equation:
FinalAmt = OriginalAmt * (1 + P)*(1 + P)*(1 + P) ...
where "P" is
  • the decimal equivalent of the percent
  • positive if the change is an increase or negative if the change is a decrease
So for your problem the equation would be:
FinalAmt = 110*(1+0.067)*(1+0.067)*(1+0.067)*(1+0.067)*(1+0.067)*(1+(-0.042))*(1+(-0.042))*(1+(-0.042))*(1+(-0.042))*(1+(-0.042))

At any point now you could use your calculator to get the answer. I am going to simplify the equation a little:
1 + 0.067 = 1.067 and 1 + -0.042 = 0.958 so now the equation is
FinalAmt = 110*1.067*1.067*1.067*1.067*1.067*0.958*0.958*0.958*0.958*0.958

If you are comfortable with exponents we could rewrite the equation as:
FinalAmt = 110%2A1.067%5E5%2A0.958%5E5
which can be rewritten as:
FinalAmt = 110%2A%281.067%2A0.958%29%5E5

I'll leave it up to you to use your calculator on any of the four versions of the equation to get an answer. (Round off your answer to the nearest whole number since we're talking about people and we don't have fractions of people.)