SOLUTION: I am trying to figure out how to line up a problem. I need to determine the percentage increase for this year's insurance rates. The rates were 152.24 last year. This year the rate

Algebra ->  Percentages: Solvers, Trainers, Word Problems and pie charts -> SOLUTION: I am trying to figure out how to line up a problem. I need to determine the percentage increase for this year's insurance rates. The rates were 152.24 last year. This year the rate      Log On


   

Question 1089039: I am trying to figure out how to line up a problem. I need to determine the percentage increase for this year's insurance rates. The rates were 152.24 last year. This year the rate is 182.76. What percentage increase does this represent? How would I write the problem in order to solve this?
Found 2 solutions by MathLover1, Theo:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let percentage increase be x% or x%2F100
if the rates were 152.24 last year, and they increase be x% of it
this year the rate is 152.24%2B%28x%2F100%29152.24
and it is equal to 182.76
so, we have
152.24%2B%28x%2F100%29152.24=182.76.......solve for x
%28152.24x%2F100%29=182.76-152.24
1.5224x=30.52
x=30.52%2F1.5224
x=20.04729374671571...round it
x=20.05 => percentage increase is 20.05%

check:
the rates were 152.24 last year
increase is 20.05% or 0.2005=>increase was 0.2005%2A152.24=30.52412
add 152.24 and 30.52412:152.24%2B30.52412=182.76 which is given this year rate

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
couple of ways to do it, all giving you the same answer.

one way.

find the difference and then divide it by the amount you are increasing from.

182.76 minus 152.24 = 30.52 / 152.24 = .20 * 100 = 20% increase.

another way.

divide the original number by the increased number and then subtract 1 from that and then multiply it by 100.

example.

182.76 / 152.24 = 1.20 minus 1 = .20 * 100 = 20% increase.

the larger number represents an increase of 20% over the smaller number.

in general, find out what the increase is and then divide that by the original number.

the actual increase factor is .200472937

i rounded it to 2 decimal digits.

note that 152.24 * 1.200472937 = 182.76

note also that 152.24 * 1.200472937 equals 152.24 * (1 + .200472937) which is equal to 152.24 * 1 + 152.24 * .200472937 which is equal to 152.24 + 30.52, which is the increase.

hope this helps.

let me know if you need more on this.