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 . . .

25x + .12 = 4.62

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.

25x + .12 = 4.62

25x=4.50

x=.18

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!

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