Dimes & Quarters - in {coins, value} space

Dimes & Quarters are two applets that represent the same problem in two different ways. Jane has 8 coins. Some are dimes and some are quarterss. Among them they have a total value of $1.55 How many dimes and how many quarters does Jane have? [answer 5 quarters, 3 dimes] One graphical representation of the problem shows the problem in the {coins,$} plane and the other graphical representation shows the problem in the {dimes,quarters} plane. Study the two representations carefully - How are the numbers of dimes and the number of quarters represented in the {coins,$} plane? How are the number of coins and the value of the coins represented in the {dimes,quarters} plane? How are the quantities $/dime and $/quarter represented in each of the two planes? Which representation do you think provides you with more insight? Why? What questions could / would you put to your students based on this applet ?