Solving a Coin Mixture Problem: Pennies and Nickels
Apply the seven-step problem-solving strategy and the total value of coins model to a coin mixture problem in which the relationship between the two coin counts involves both multiplication and addition.
Problem: Danny has $2.14 worth of pennies and nickels in his piggy bank. The number of nickels is two more than ten times the number of pennies. How many nickels and how many pennies does Danny have?
- Read: The coins are pennies (worth $0.01) and nickels (worth $0.05). Total value is $2.14.
- Identify: Find the number of pennies and nickels.
- Name: Let = the number of pennies. The number of nickels is . Organize in a table:
| Type | Number | Value ($) | Total Value ($) |
|---|---|---|---|
| Pennies | 0.01 | 0.01p | |
| Nickels | 0.05 | ||
| Total | 2.14 |
- Translate: Add the total values to equal the overall total: .
- Solve:
- Distribute:
- Combine terms:
- Subtract 0.10:
- Divide by 0.51:
- Find nickels:
- Check: 4(0.01) + 42(0.05) stackrel{?}{=} 2.14 -> . checkmark
- Answer: Danny has 4 pennies and 42 nickels.
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Elementary Algebra @ OpenStax
Ch.3 Math Models - Elementary Algebra @ OpenStax
Algebra
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Prealgebra
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In a professional cash-handling environment, what is the standard procedure for determining the overall value of a collection that contains several different types of coins, such as quarters, dimes, and nickels?
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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?
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Learn After
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Standardizing Algebraic Models for Cash Audits
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