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Example: Solving a Coin Mixture Problem with Quarters and Nickels
Apply the problem-solving strategy to find the number of each type of coin based on their total value and a relationship involving multiplication and addition.
Problem: Jesse has $6.55 worth of quarters and nickels in his pocket. The number of nickels is five more than two times the number of quarters. How many nickels and how many quarters does Jesse have?
- Read: The coins are quarters (worth $0.25) and nickels (worth $0.05). The total value is $6.55.
- Identify: Find the number of quarters and nickels.
- Name: Let = the number of quarters. The number of nickels is .
| Type | Number | Value ($) | Total Value ($) |
|---|---|---|---|
| Quarters | |||
| Nickels |
- Translate: Add the total values to equal $6.55:
- Solve:
- Distribute :
- Combine like terms:
- Subtract from both sides:
- Divide both sides by : Find the number of nickels:
- Check: Does ?
- Answer: Jesse has quarters and nickels.
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OpenStax
Intermediate Algebra @ OpenStax
Ch.2 Solving Linear Equations - Intermediate Algebra @ OpenStax
Algebra
Related
A store manager is reconciling the daily receipts and needs to organize a count of various coins. According to the standard problem-solving strategy for coin word problems, which four labels should be used as the headers for the organizational table?
A retail supervisor is training a new cashier on how to calculate the number of specific coins in a till when only the total value and a relationship between the coin counts are known. Arrange the following steps of the coin problem-solving strategy in the correct chronological order.
A small business owner is using the standard seven-step strategy to solve a coin-related word problem for their monthly cash report. Match each column header from the organizational table to the specific type of data it should contain.
A retail supervisor is training a new cashier on how to use an organizational table to solve coin-related word problems for a cash drawer reconciliation. True or False: In the 'Translate' step of this strategy, the final equation is created by summing the entries in the 'Total Value' column of the table.
Procedural Calculation in the Coin Strategy
Finalizing a Professional Cash Reconciliation
A retail supervisor is training a new cashier to use an organizational table for cash drawer audits. They explain that the entry in the 'Total Value' column for any specific coin type is always found by multiplying the 'Number' of those coins by the ____ of a single coin.
Documenting the Coin Reconciliation Strategy
A payroll administrator is using a specialized seven-step strategy to reconcile a petty cash account containing nickels and dimes. During the 'Check' step of this process, where is it most appropriate to verify the calculated result to ensure that the initial translation of the problem into an equation was accurate?
An office manager is using the seven-step problem-solving strategy to reconcile a petty cash drawer containing various denominations. After the manager has successfully solved the algebraic equation and verified that the result is logical, what is the final step required to complete the strategy?
Example: Solving a Coin Mixture Problem with Quarters and Nickels
Example: Solving a Coin Mixture Problem with Dimes and Nickels
Ticket and Stamp Mixture Problems
Example: Solving a Stamp Mixture Problem with 49-Cent and 35-Cent Stamps
Example: Another Stamp Mixture Problem with 49-Cent and 35-Cent Stamps
Example: Solving a Stamp Mixture Problem with 49-Cent and 20-Cent Stamps