How many pencils are used in the state of California in one year?

1.  Background Story

Have you ever thought about how many pencils you use in a year? Well how about the entire state of California? How many pencils does California go through in a year? I chose this question because I was thinking about how everyone uses pencils, but no one keeps track of how many they use. Especially a entire state. Also, people may say this pencils lasted them a while, but do they know for how long? Now lets see what we can find.^[a]

2.  Ask Yourself This: 

Lets think about what we need to know in order to solve the problem. What is the population of California? How long is the average life of a pencil? How long is a year in months?^[b]

3.  Helpful Hints:  I will give you some hints for you to help out in your research in solving this question.

1. Population of California is 38,041,430. Source: http://populationofcalifornia.blogspot.com/2013/03/population-of-california-in-2013.html
2. The average pencil life is about 2 months.
3. One year is 12 months.

For the average life of a pencil, I remember how many pencils I use in a 12 pack of pencils last year. I used about half of them, so if I used 6 pencils a year that means the average life of a pencil is about 2 months.^[c]

4.  Construct a Formula

First, get the population of California, the average life of a pencil, and remember how long a year is in months. Now times the population of CA by the approximate lifespan of a pencil to get how many pencils are used in 2 months by CA. Then times the new number by 3 for the 6 months that you’re finishing a pencil to get the approximate amount of pencils California uses in a year.

c X p X 3 = 228,248,580 pencils/year in CA

c = pop. of CA        p = life of pencil (2 months)

^[d]

5.  Messy Math

Here is how I solved the problem.

1 pencil/2 months                              X 1 year      = 1 year         

3.804143 X 107 pencils used in CA X 6 pencils/2 months = 228,248,580 pencils used in CA        

3.804143 X 107 = 38,041,430

3.804143 X 107 = Both pencils used in California (for 2 months) AND California’s population.

228,248,580 = 2.2824858 X 108 ← Answer^[e]

6.  Answer

So here’s what I found. I found out that if everyone in California uses a pencil and replaces that pencil every 2 months for every year, just the state of California would use an approximate of 228,248,580 pencils every year. Who knows what the entire U.S. uses in a year or even the world. I’ll let you figure that out.^[f]