A jar of coins contains nickels, dimes, and quarters. The total number of coins is 8 and the total value is $1.45. How many of each coin are there? Nickels: 0 Dimes: 0 Quarters: 0
A jar of coins contains nickels, dimes, and quarters. The total number of coins is 8 and the total value is $1.45. How many of each coin are there? Nickels: 0 Dimes: 0 Quarters: 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![### Coin Counting Problem
**Problem Statement:**
A jar of coins contains nickels, dimes, and quarters. The total number of coins is 8, and the total value is $1.45. How many of each coin are there?
**Solution Workspace:**
- **Nickels:** 0
- **Dimes:** 0
- **Quarters:** 0
**Strategy for Solving the Problem:**
1. **Define Variables:**
- Let \( N \) be the number of nickels.
- Let \( D \) be the number of dimes.
- Let \( Q \) be the number of quarters.
2. **Equations from the Problem:**
1. The total number of coins:
\[ N + D + Q = 8 \]
2. The total value of the coins:
\[ 0.05N + 0.10D + 0.25Q = 1.45 \]
3. **Method for Solving:**
- Use the first equation to express one variable in terms of the others.
- Substitute into the second equation to solve for the variables.
You can proceed with the solution by setting up a system of linear equations or using guess-and-check in a structured mathematical approach.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd936c6c0-8e3b-4a92-9646-2c460fec57ae%2F184841eb-6bae-40bf-8ce8-97739bcebbc9%2Fqv3ie2k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Coin Counting Problem
**Problem Statement:**
A jar of coins contains nickels, dimes, and quarters. The total number of coins is 8, and the total value is $1.45. How many of each coin are there?
**Solution Workspace:**
- **Nickels:** 0
- **Dimes:** 0
- **Quarters:** 0
**Strategy for Solving the Problem:**
1. **Define Variables:**
- Let \( N \) be the number of nickels.
- Let \( D \) be the number of dimes.
- Let \( Q \) be the number of quarters.
2. **Equations from the Problem:**
1. The total number of coins:
\[ N + D + Q = 8 \]
2. The total value of the coins:
\[ 0.05N + 0.10D + 0.25Q = 1.45 \]
3. **Method for Solving:**
- Use the first equation to express one variable in terms of the others.
- Substitute into the second equation to solve for the variables.
You can proceed with the solution by setting up a system of linear equations or using guess-and-check in a structured mathematical approach.
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