Journey North: Symbolic Monarch Butterfly Migration

Challenge Question # 2:
How Was This Estimate Calculated from the Clues?

To estimate the number of Symbolic Butterflies from the clues, there were three questions you needed to answer :

1) What was the number of envelopes processed per hour?

2) What was the total number of hours spent processing envelopes?

3) What was the number of butterflies in each envelope?

4) Calculating the Estimated Total Number of Butterflies

With these questions answered, you would have the three key numbers needed to calculate the estimated number of butterflies. How? Read below.

1) What was the number of envelopes processed per hour?
This figure was able to be calculated by looking at the rate of processing on Days One and Two:

By DIVIDING the number of envelopes processed during Days One and Two (581.5 envelopes) by the total hours spent processing on on those days (30 hours), you learn the rate of envelopes processed per hour = 19.383 Envelopes per Hour

2) What was the total number of hours spent processing envelopes?
This will be the total hours spent processing during Days One and Two, PLUS the additional hours processing after Days One andTwo.

-We know that the 30 hours spent processing on Days One and Two was 25% of the total time spent processing, because the clues tell us that that additional time spent processing butterflies after Days One and Two was equal to 75% of all time processing butterflies.

-To find out how many additional hours were spent after Days One/Two, you MULTIPLY 30 hours (total Days One/Two time) BY 3 (30 hours times 3 = 90). This is because the percentage of hours spent after Days One and Two is 75% of all time, which is three times the percentage of time spent on Days One and Two (25%). The answer of 90 hours is the amount of hours spent After Days One/Two.

- Add the Days One/Two hours (30) PLUS the total After Days One/Two hours (90), and the answer is: 120 hours is the total of all hours spent processing.

3) What was the number of butterflies in each envelope?
Clues tell us that there were approximately 21.61 butterflies in each envelope.

4) Calculating the Estimated Total Number of Butterflies:

With the three numbers above, here is how you calculate the estimated total number of butterflies processed and headed for Angangueo:

120 total processing hours MULTIPLIED BY 19.383 Envelopes per hour = 2326 Total Envelopes processed (rounded from 2,325.96)
2326 Total Envelopes MULTIPLIED BY 21.61 butterflies per envelope = 50,268 estimated total butterflies
2326 Total Envelopes MULTIPLIED BY 21.61 butterflies per envelope =
~ 50,264.86 butterflies. Of course, there was some averaging and rounding of numbers in the math process, so this caculation is a close estimate--we actually counted 50,268 butterflies at the time we prepared the butterflies to fly south.