0. A coin jar contains 425 coins all are pennies, nickels and dimes (1c, 5cand 10c) with total value $21.12. If there are 100 more nickels than dimes, find the nnumber of each types of coins in the jar.

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Problem 10:**

A coin jar contains 425 coins, all of which are pennies, nickels, and dimes (1¢, 5¢, and 10¢ respectively) with a total value of $21.12. If there are 100 more nickels than dimes, find the number of each type of coin in the jar.

---

**Explanation:**

To solve this problem, we can set up equations based on the information given:

1. Let \( p \) be the number of pennies, \( n \) be the number of nickels, and \( d \) be the number of dimes.
2. The total number of coins equation: 

   \[
   p + n + d = 425
   \]

3. The total value equation in cents:

   \[
   1p + 5n + 10d = 2112 \quad (\text{since $21.12 = 2112 cents})
   \]

4. The relationship between nickels and dimes:

   \[
   n = d + 100
   \]

Using these equations, the problem can be solved using algebraic methods to find the values of \( p \), \( n \), and \( d \).
Transcribed Image Text:**Problem 10:** A coin jar contains 425 coins, all of which are pennies, nickels, and dimes (1¢, 5¢, and 10¢ respectively) with a total value of $21.12. If there are 100 more nickels than dimes, find the number of each type of coin in the jar. --- **Explanation:** To solve this problem, we can set up equations based on the information given: 1. Let \( p \) be the number of pennies, \( n \) be the number of nickels, and \( d \) be the number of dimes. 2. The total number of coins equation: \[ p + n + d = 425 \] 3. The total value equation in cents: \[ 1p + 5n + 10d = 2112 \quad (\text{since $21.12 = 2112 cents}) \] 4. The relationship between nickels and dimes: \[ n = d + 100 \] Using these equations, the problem can be solved using algebraic methods to find the values of \( p \), \( n \), and \( d \).
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