Estimating Your Way to a Jelly Bean Victory

A popular fundraiser is to guess how much of a certain object are in a container. Often this object is sweet, sweet candy. The person with the closest guess wins the candy-filled container. Increase your odds of winning by making an educated guess! An educated guess is simply an estimate.

Let's say there is a jar filled with jelly beans. How many jelly beans does the jar contain?

First, estimate the size of the jar to determine its volume. You pull out the cell phone in your pocket that you guess is about six inches tall. Using it to estimate the dimensions of the jar, you determine the height is about one-and-a-half cell phones and the diameter is one cell phone. Using the volume of the cylinder you calculate the volume of the jar to be about 254 cubic inches. Using the same logic you intuitively estimate that a jelly bean has a diameter of 0.5 inches and a length of 0.75 inches. Estimating the volume of a jelly bean using a cylinder you find the volume of a single jelly bean to be 0.15 cubic inches.

Then it is a simple matter of dividing the volume of the jar by the volume of a single jelly bean to find that about 1,693 jelly beans could fit in the jar. But what about the gaps between the jelly beans? Great point! Various sources estimate the jar contains 20% air by volume [1][2]. Use proportions to calculate how many jelly beans would take up 80% of the jar by volume.

How sweet is that? Give this technique a whirl at your next fundraiser. Who knows, your math wizardry may help you walk away with a jar full of jelly beans!

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[1] "How to win a guess the number of jelly beans contest". How Tutorial. WordPress. 18 April 2011. Web. 31 July 2016.
[2] "How to Win a Jellybean Guessing Contest". Cleverness: Getting Diggy with It. WordPress. 07 March 2007. Web. 31 July 2016.