Question

In a bag, a child has 325 coins worth $\$ 19.50$ . There were three types of coins: pennies, nickels, and dimes. If the bag contained the same number of nickels as dimes, how many of each type of coin was in the bag?

Name: Problem 60, Chapter 7: College Algebra
Uploaded: 2019-07-19T21:48:31-08:00
Duration: 2 min 44 s
Channel: Matt Bremer
Description: In a bag, a child has 325 coins worth 19.50 . There were three types of coins: pennies, nickels, and dimes. If the bag contained the same number of nickels as dimes, how many of each type of coin was in the bag?

   In a bag, a child has 325 coins worth $\$ 19.50$ . There were three types of coins: pennies, nickels, and
dimes. If the bag contained the same number of nickels as dimes, how many of each type of coin was
in the bag?

College Algebra

Jay Abramson 1st Edition

Chapter 7, Problem 60

Instant Answer

Solved by Expert Matt Bremer

07/19/2019

Step 1

We know that the total number of coins is 325, so we can write the first equation as: \[x + y + z = 325\] Show more…

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In a bag, a child has 325 coins worth $\$ 19.50$ . There were three types of coins: pennies, nickels, and dimes. If the bag contained the same number of nickels as dimes, how many of each type of coin was in the bag?

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Key Concepts

Word Problem Translation

This involves reading a real-world scenario and converting it into mathematical expressions or equations by defining variables and relationships. It is crucial for understanding how to model the problem mathematically.

System of Linear Equations

This concept deals with setting up and solving multiple equations simultaneously, as the problem provides several conditions (such as total count and total value) that must all be satisfied at the same time.

Variable Substitution

A method used to simplify a system of equations by expressing one variable in terms of another, which reduces the number of variables and makes the problem more tractable.

Linear Diophantine Equations

These are equations where only whole number (integer) solutions are acceptable. This concept is key in problems involving counts of items, ensuring that the solutions are practical and meaningful in real-world contexts.

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