Question

You have 744 coins in nickels, dimes, and quarters with a combined value of $129! There are twice as many quarters as dimes. The bank is requiring you wrap the coins to make a deposit in a paper roll. Each paper roll of quarters can hold $10. Without spending time to count all the quarters, you have your calculator with you in your backpack! How many quarter paper rolls do you need to request at the bank? Show your work!

Answer 1

To find out how many quarter paper rolls to request at the bank, we need to determine the total value of quarters. Let's represent the number of dimes as 'd' and the number of quarters as 'q'. Using the given information and substitution, we find that we need 1 paper roll for the 40 quarters.

Step-by-step explanation:

To find out how many quarter paper rolls to request at the bank, we need to determine the total value of quarters. Let's represent the number of dimes as 'd' and the number of quarters as 'q'. Since there are twice as many quarters as dimes, we can write the equation: q = 2d. We also know that the total value of the coins is $129. The value of each nickel is $0.05, each dime is $0.10, and each quarter is $0.25. So, the equation for the total value of the coins is: 0.05(n) + 0.10(d) + 0.25(q) = 129.

We can substitute '2d' for 'q' in the equation and simplify:

0.05(n) + 0.10(d) + 0.25(2d) = 129

0.05n + 0.10d + 0.50d = 129

0.05n + 0.60d = 129

Now, we can solve the equation to find the values of 'n' and 'd'.

We can use a calculator to substitute different values for 'n' and 'd' until we find a combination that satisfies the equation. The values that work are n = 580 and d = 40.

Therefore, there are 580 nickels, 40 dimes, and 80 quarters.

Now, let's calculate how many quarter paper rolls we need. Each paper roll can hold $10 worth of quarters. Since each quarter is worth $0.25, there are 40 quarters, which is equivalent to $10. So, we need 1 paper roll for the 40 quarters.