Learn Before
Example: Solving a Coin Mixture Problem with Dimes 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 subtraction.
Problem: Elane has $7.00 total in dimes and nickels in her coin jar. The number of dimes that Elane has is seven less than three times the number of nickels. How many of each coin does Elane have?
- Read: The coins are nickels (worth $0.05) and dimes (worth $0.10). The total value is $7.00.
- Identify: Find the number of nickels and dimes.
- Name: Let = the number of nickels. The number of dimes is .
| Type | Number | Value ($) | Total Value ($) |
|---|---|---|---|
| Nickels | |||
| Dimes |
- Translate: Add the total values to equal $7.00:
- Solve:
- Distribute :
- Combine like terms:
- Add to both sides:
- Divide both sides by : Find the number of dimes:
- Check: Does ?
- Answer: Elane has nickels and dimes.
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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
Learn After
An office manager is performing a petty cash audit of a coin box containing only nickels and dimes. To calculate the total value of the coins algebraically, the manager uses to represent the number of nickels. Match each component of the coin mixture calculation to its correct mathematical representation based on the problem-solving strategy.
A retail supervisor is training an apprentice to audit a cash drawer containing nickels and dimes totaling 7.00 dollars. In this specific scenario, the number of dimes is seven less than three times the number of nickels (). Arrange the steps in the correct logical order to determine the quantity of each coin, following the problem-solving strategy from the course example.
A retail cashier is reconciling a petty cash drawer that contains only nickels and dimes. The cashier notes that the number of dimes is exactly seven less than three times the number of nickels (). When setting up a calculation to find the total value of the money in the drawer, which expression correctly represents the total dollar value of the dimes?
A retail supervisor is auditing a coin jar that contains nickels and dimes totaling 7.00 dollars. The supervisor determines that the number of dimes is 'seven less than three times' the number of nickels (). True or False: To represent the quantity of dimes correctly in an algebraic equation, the supervisor should use the expression .
A retail manager is setting up an algebraic equation to audit a bag of mixed nickels and dimes. Following the standard problem-solving strategy, if the manager uses to represent the quantity of nickels, what decimal coefficient must be multiplied by to represent the total dollar value of these nickels?