$25 million is 11.6% more than they paid for previous years, what did they pay last year

Question

due to increase mailing costs, the new rate will cost $25 million, this is 11.6% More than paid than previous years, how much did it cost last year 

Answer 1

Danielle, let "x" stand for the cost last year. Then 25 million must equal the same quantity as what we get if we "let x increase by 11.6%"

 

But x increased by 11.6% equals x * 1.116 (where * stands for multiplication)  therefore:

 

25,000,000 = x * 1.116

 

Hence x = 25,000,000 / 1.116 which your calculator can find to be about 22,401,433.69

 

CHECK your answer: Does 22,401,443.69, if increased by 11.6%, result in 25,000,000? Try it:

 

22,401,443.69 + (0.116)* 22,401,443.69

 

or 22,401,443.69 times 1.116 and you will get almost exactly 25M (not exactly because we rounded to 69 cents from "69 plus fractions of a penny" in estimating decimal for x from "25,000,000 / 1.116"

 

NOTE/WARNING: Answer to "this year's price is 100, after last year's price went up by 25%" will NOT have the same answer as "take 25% off from this year's price" so you will not get the correct answer by just subtracting away 11.6% from 25M.

 

In this second example, just to illustrate the old price was NOT 75 dollars (which would be result of taking 25% off from 100) but rather x*1.25 = 100 so x=80. Check it: 80 increased by 25% is "80 plus a quarter of 80" which is 80+20 which is this year's 100 dollars.

Answer 2

Dr. B is absolutely right! I am retracting my solution to avoid confusion. Good luck!