The Problem

For every two pollywogs I buy at the regular price, I get a third pollywog for a penny. I spent $4.62 for 37 pollywogs. Find, in cents, the regular price of one pollywog.
(Source: Adapted from Mathematics Teaching in the Middle School, Sep-Oct1996)

The Solution

We can think about buying pollywogs in groups of three, since every two bought at full price you can get one for $0.01. Since a total of 37 pollywogs were bought, we can think of the purchase as 12 groups of three and one pollywog by itself. Since we know that we have 12 full groups of three pollywogs, that tells us that 24 pollywogs were purchased at full price in additon to the one left over, for a total of 25 pollywogs purchased at full price. We also know that there were 12 pollywogs that cost only $0.01. So, we can write the following equation to solve for the cost of each full price pollywog, letting p=price of each pollywog:

25p + 0.12 = 4.62

25p = 4.50

p = $0.18

Thus we discover that each full price pollywog costs $0.18.