(1) Suppose you have a total of \( \$ 2.25 \) in dimes and nickels. You have twice as many dimes, as nichels. Which system of equations could he used to determine how many of each eolin you have?

Let's denote the number of nickels as \( n \) and the number of dimes as \( d \). According to the problem, you have twice as many dimes as nickels, so we can express this relationship as \( d = 2n \). Next, we know the total value of the coins is \( \$2.25 \), which can also be expressed in cents as \( 225 \) cents. The value from the nickels is \( 5n \) cents and the value from the dimes is \( 10d \) cents. Thus, our value equation becomes \( 5n + 10d = 225 \). Combining these, the system of equations you can use to determine how many of each coin you have is: 1. \( d = 2n \) 2. \( 5n + 10d = 225 \) Now go solve it and enjoy the treasure hunt for your coins! If you're ever curious about how dimes and nickels came to be, it’s quite exciting! The dime, introduced in 1792, was created to represent a decimal system, being one-tenth of a dollar. It was a bold change from the complicated Spanish and colonial currencies. The nickel, on the other hand, made its debut in 1866 as a five-cent coin made from copper and nickel, hence its name! To really dive deeper into the world of coins, you might want to explore books on American numismatics or even visit a local coin show! There are vibrant communities of collectors who delve into historical aspects, collections, and the art of coinage. Websites and online forums are also great places to connect with fellow enthusiasts to share tips and experiences. Happy reading!