Solving a Nickels and Quarters Mixture Problem Using a System of Equations
Apply the seven-step problem-solving strategy and a table to solve a coin mixture application involving nickels and quarters using a system of linear equations.
Problem: Priam has a collection of nickels and quarters, with a total value of $7.30. The number of nickels is less than three times the number of quarters. How many nickels and how many quarters does he have?
- Read the problem. A table will help organize the information.
- Identify what to find: the number of nickels and the number of quarters.
- Name the unknowns. Let the number of nickels and the number of quarters. Organize the data into a table:
| Type | Number | Value ($) | Total Value ($) |
|---|---|---|---|
| Nickels | |||
| Quarters | |||
| Total |
-
Translate into a system of equations.
- The "Total Value" column gives the first equation:
- The relationship between the quantities (nickels is less than three times quarters) 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 $2.55. quarters at $0.25 each is $4.75.
-
Answer the question. Priam has nickels and quarters.
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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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