Questions: How many ways can you make change for 30 using only nickels, dimes, and quarters?

How many ways can you make change for 30 using only nickels, dimes, and quarters?
Transcript text: How many ways can you make change for $30 using only nickels, dimes, and quarters?
failed

Solution

failed
failed

Solution Steps

To solve this problem, we need to find the number of combinations of nickels, dimes, and quarters that sum up to 30 cents. We can use a nested loop approach where we iterate over possible counts of each coin type and check if their total value equals 30 cents.

Step 1: Define the Problem

We need to determine the number of ways to make change for \(30\) cents using only nickels (\(5\) cents), dimes (\(10\) cents), and quarters (\(25\) cents).

Step 2: Set Up the Equation

Let:

  • \(n\) = number of nickels
  • \(d\) = number of dimes
  • \(q\) = number of quarters

The equation representing the total value of the coins is: \[ 5n + 10d + 25q = 30 \]

Step 3: Count the Combinations

By iterating through all possible values of \(n\), \(d\), and \(q\) that satisfy the equation, we find that there are \(5\) valid combinations of these coins that total \(30\) cents.

Final Answer

The total number of ways to make change for \(30\) cents using nickels, dimes, and quarters is \\(\boxed{5}\\).

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
When a marketing website collects cookies, marketers should commit to best practices for privacy and security. The sponsoring organization may also be required to conform to World Wide Web Consortium (WC3) standards, obtain consumer consent, create multiple versions of the site, improve page-loading speeds.
failedAnswered
Our bodies can not make starch, but we often eat food that contains starch. Our body breaks down starch into can be used by our body.
failedAnswered
In an actual cost system, it is difficult to obtain timely information about the: a. direct labor cost per unit. b. overhead cost per unit. c. cost of direct materials consumed per unit. d. All of these choices are correct.
failedAnswered
The image contains a hand-drawn matrix or grid-like structure with rectangular boxes or cells arranged in rows and columns. There are also two lines drawn horizontally across the grid - one red line separating the top row from the rest, and one line at the bottom that appears incomplete. Additionally, there are some numerical digits (3, 2, 1) written inside a few of the cells towards the bottom of the grid structure.
failedAnswered
Find the area of the shaded region inside the square and between the two circles. Use π ≈ 3.14. The area of the shaded region is approximately □ m^2 (Type an integer or decimal)