Quandaries
and Queries 

If the number of toonies required to buy a book is nine more than the number of fivedollar bills required to buy the same book, determine the cost of the book. 

Hi Dorly, I can see two ways to approach this problem. First you can just look at the numbers and use the "guess and check" method. You can buy the book with toonies and no change so the price of the book is divisible by 2. You can buy the book with fivedollar bills and no change so the price of the book is divisible by 5. Thus the price of the book is divisible by 10 and hence the book costs $10, or $20, or $30, or $40, ... For each of these see how many toonies that would be and how many fivedollar bills that would be and find the one where it takes nine more toonies than fivers. The second method is to use some algebra. Suppose it costs T toonies to buy the book and F fivers to buy the book. Thus the book costs
that is
You also know
And hence
Solve for F. Penny


