A Day at the Fairs
The problem this week is an old one, in fact over 500 years old. It goes back to the days in Europe when fairs were common in many cities, and merchants would travel from city to city, selling their various goods and buying other items they desired.
It seems that a humble merchant visited three fairs. At the first fair, early in the morning, he doubled his money selling his products, but spent $30 in food and buying other items. (Note:to make things easier to write, we will use the dollar sign for the unit of money.)
It seems that a humble merchant visited three fairs. At the first fair, early in the morning, he doubled his money selling his products, but spent $30 in food and buying other items. (Note:to make things easier to write, we will use the dollar sign for the unit of money.)
At midday at the second fair, he tripled his money and spent $54. At the third fair in the afternoon he quadrupled his money but spent $72.
Upon his return home to his wife and ten children, late that day, he counted the money he had in his bag; there was $48.
Did the man return richer or poorer than when he left? And how much did the man gain or lose, respectively?
Extra:If you did your work straightforwardly, your next-to-last step of equation work was of the form Ax = B. The number B is in some way rather interesting; what is it?
Submissions are due by the end of the day on April 27 Make sure to scan your work and put it in your Mathematics/POW folder with a name of LASTNAMEWeek17. See me with questions. You may work with a partner but make sure you note that on your submission and you both must submit a copy for credit. You also must explain your process and solution in sentences!
