Intermath: Investigations: Number Concept: Fractions

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.

At first this question seems a little tricky. After some thought you will see that it is easier than you may have believed. The best thing to focus on is the very first sentence - when you buy two, you get one free. So think about buying the pollywogs in groups of three (the 2 you pay for + the one that's free). Imagine it . . .

these 2 full price & that one for a penny. There are three pollywogs that you just bought. How many groups of three pollywogs did I buy? Well I bought 37 pollywogs total, so I bought 12 groups of three pollywogs - but that is only 36 pollywogs. I actually bought 12 groups of three pollywogs plus one more lonely pollywog, which I had to pay full price for. So out of the the three pollywogs I bought in each group, one only cost 1 cent. I had 12 groups, each of which had a pollywog that I paid a penny for, so I spent 12 cents for those 12 pollywogs. But the remaining 25 pollywogs, I paid full price. Now, I bet you are ready to write an equation. Are you thinking . . .

So what I said there was the number of pollywogs at full price (x) times that price plus the 12 cents for the other 12 pollywogs that cost a penny each will equal the total amount I spent on pollywogs. So let's solve the equation that we created.

Now we know that each regular price pollywog we bought was only 18 cents. Seems pretty cheap to me for one of those cute little pollywogs!