Proportional Reasoning

Question

7.1

 

In your pocket, you have 15 to 20 coins: dimes, nickels, quarters, and pennies. You reach into your pocket, pull out a coin, record it, and put it back into your pocket. After repeating this 50 times, here are the results:


Coin        Times selected      

Penny             28
Nickel              8
Dime              10

Quarter            4 


Based on your findings, what would be a reasonable number of pennies, nickels, dimes, and quarters that are actually in your pocket?


Explain how you arrived at your conclusion. Justify your answer using proportional reasoning.

Answer 1

To start with, assume 20 coins because it makes the math easier.

20 is 40% of 50, so multiply each of the numbers by .4:

 

28 * .4 = 11.2 pennies

8 * .4 = 3.2 nickels

10 * .4 = 4 dimes

4 * .4 = 1.6 quarters

 

If we round each to the nearest whole number, we end up with exactly 20 coins and a theoretical probability that is very near the observed results.

 

11 pennies

3 nickels

4 dimes

2 quarters

 

It could be argued that the variation in size of the coins skew the theoretical probability, but since they didn't offer any information about the sizes, I doubt that is part of this problem.