What is the overall percent decrease?

Question

Suppose the price of a certain item decreases by 5.1% a total of 5 times, and then increases by 1.4% a total of 3 times. By what overall percent did the price decrease?

Answer 1

Suppose the original price is p.  A decrease of 5.1% brings the price down to 0.949p.  Do this 5 times in a row and you get (0.949)⁵p. 

 

Next, increase the result by 1.4% three times in a row, and the new result is (1.014)³[(0.949)⁵p].

 

Finally, take the difference between original and final price, divide by the original price, and multiply by 100 to get the % decrease. 

 

% decrease = 100 {p - (1.014)³[(0.949)⁵p]} / p = 100[1 - (1.014)³(0.949)⁵] ≅ 19.75%