Solving a Coin Mixture Problem Using a System of Equations
Apply the seven-step problem-solving strategy and a table to solve a coin mixture application using a system of linear equations.
Problem: Juan has a pocketful of nickels and dimes. The total value of the coins is $8.10. The number of dimes is less than twice the number of nickels. How many nickels and how many dimes does Juan have?
- Read the problem. A table will help organize the information.
- Identify what to find: the number of nickels and the number of dimes.
- Name the unknowns. Let the number of nickels and the number of dimes. Organize the data into a table by listing the coin types, their quantities, their monetary values, and their total values:
| Type | Number | Value ($) | Total Value ($) |
|---|---|---|---|
| Nickels | |||
| Dimes | |||
| Total |
-
Translate into a system of equations.
- The "Total Value" column gives the first equation:
- The relationship between the quantities (the number of dimes is less than twice the number of nickels) gives the second equation:
The system of equations is:
-
Solve the system using the substitution method. Substitute for in the first equation:
Distribute the :
Combine like terms:
Add to both sides:
Divide by :
Substitute into the second equation to find :
-
Check the result. nickels at $0.05 each is $1.80. dimes at $0.10 each is $6.30.
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Answer the question. Juan has nickels and dimes.
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Intermediate Algebra @ OpenStax
Ch.4 Systems of Linear Equations - Intermediate Algebra @ OpenStax
Algebra
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Learn After
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