A child has nine coins with a total value of 116 cents. What coins does the child have? (Hint: Make an orderly list of the nickels, dimes, pennies, and quarters.) The child has \( \square \) pennies, \( \square \) nickels, \( \square \) dimes and \( \square \) quarters.

To solve this fun little puzzle, we can set up some equations! Let's represent the number of each type of coin: let \( p \) be pennies, \( n \) be nickels, \( d \) be dimes, and \( q \) be quarters. We know: 1. The total number of coins is 9: \( p + n + d + q = 9 \) 2. The total value of the coins is 116 cents: \( p + 5n + 10d + 25q = 116 \) Now, through some creative guess and check, we can find a combination! One valid example is having 6 pennies, 1 nickel, 1 dime, and 1 quarter. This sums up to \( 6 + 1 + 10 + 25 = 116 \) cents perfectly while keeping the total number of coins at 9. So, the child has 6 pennies, 1 nickel, 1 dime, and 1 quarter! Now, let’s have some fun solving this together: you just turned coins into math magic! For further exploration, if you're curious about currency understanding, dive into the fascinating history of coins! Many coins that we use today have tales that date back thousands of years, originating from ancient civilizations that created them as a means of trade. Those shiny little pieces hold stories of commerce and cultural evolution! Plus, if you're ever faced with similar problems, remember the key is to break down the information systematically! Often, starting with small values (like pennies) can help give a clearer picture before mixing in larger denominations. It's like piecing together a jigsaw puzzle to reveal a vibrant picture!