Let's begin with some relatively easy problems. The challenges become gradually more difficult as you go through the book. The problems in this chapter can be solved without advanced mathematics. Knowledge of basic arithmetic, algebra, and geometry will be helpful, as well as your own creative thinking. I recommend that you attempt all the problems, even if you already know the answers, because you may discover new and interesting aspects of the solutions. A bonus after each solution discusses a related mathematical topic. Remember, each problem has an aha! solution.

Arithmetic

Fair Division

Abby has fifteen cookies and Betty has nine cookies. Carly, who has no cookies, pays Abby and Betty 24 cents to share their cookies. Each girl eats one-third of the cookies.

Betty says that she and Abby should divide the 24 cents evenly, each taking 12 cents. Abby says that since she supplied fifteen cookies and Betty only nine, she should take 15 cents and Betty 9 cents.

What is the fair division of the 24 cents between Abby and Betty?

Solution

The key is to determine the worth of one cookie. Each girl eats eight cookies. Since Carly pays 24 cents for eight cookies, each cookie is worth 3 cents. Thus Abby, who starts with fifteen cookies and sells seven to Carly, should receive 21 cents, and Betty, who starts with nine cookies and sells one to Carly, should receive 3 cents.