Percentage question.

Question

Catherine loves pickles so much that after returning from Roger's Market with some pickles, she eats 45% of the pickles she just bought. The next day she eats 45% of the remaining pickles and continues to eat another 45% each day. What percent of the pickles will Catherine have left after four days? (Round your answer to the nearest whole percent.)

Answer 1

Hi Jessica (and Sherry),

 

I think the answer is somewhat different:

 

Day One:    1 - 0.45  = 0.55 remain

 

Day Two:  Eats 0.45 of the 0.55, so amount left is now:

              0.55 - 0.55*0.45 = 0.55 (1-0.45) = 0.55 * 0.55

 

Since she eats 45% each day, that means that 55% from that day remains,

so continuing:

 

Day Three:  ...  = 0.55 * 0.55 * 0.55

 

Day Four:  = 0.55 * 0.55 * 0.55 * 0.55

  which is 0.0915, or  9 % to the nearest %.

 

Answer 2

Assuming Day One is the day she buys the pickles... And we are talking about the amount LEFT.

 

Day One:     1 - 0.45        

Day Two:     1 - 0.45 - 0.45²

Day Three:  1 - 0.45 - 0.45² - 0.45³

Day Four:    1 - 0.45 - 0.45² - 0.45³ - 0.45⁴

= 1- 0.45 - 0.2025 - 0.091125 - 0.04100625 

= 0.21536875 = 21.536875 = 22% when rounded to the nearest percent