Dear Students,

The past three years the math department has kept a gargantuan glass jar full of pennies that we find in the hallway. The jar is now too full to add any more pennies. Just as I was preparing to take the pennies to the bank to be counted, Ms. Rafanti stopped me and explained to me that there may be some wheat pennies in the jar. She went on to say that wheat pennies are actually worth more than a penny but the bank’s counter will not distinguish between the two. Since none of us are willing to count the pennies but all of us are looking forward to spending them (for the good of the department that is) I’m taking them to the bank to be counted. What information would I need to determine whether or not there were any wheat pennies present, and if so, how many there were?

(Hint: Pennies minted between 1959 and 1981 are composed of 95% copper and 5% zinc with and average weight of 0.030N, or a mass of 3.11g. Pennies minted from 1983 on are composed of 99.2% zinc and 0.8% copper with an average weight of 0.0245N.)

Teacher notes:

Students may offer a wide range of methods for answering the question. A system of equations may provide an efficient method given the weight of one wheat penny, one non wheat penny, the total weight of all the coins, and the number of coins in the jar.

The system might be solved as follows:

Let N = total number of pennies

Let T = total weight of all pennies

Let a = the number of post 1981 pennies

Let b = the number pennies minted between 1959 and 1981

a + b = N

2.5a + 3.11b = T

This lab would serve students well as a review of systems of equations. In a class where students are eager to experience new types of problems without being led by example, take out any reference above to writing equations and do this lab at the beginning of a unit on systems of equations.