Solving a Quarters and Dimes Mixture Problem Using a System of Equations
Apply the seven-step problem-solving strategy and a table to solve a coin mixture application involving quarters and dimes using a system of linear equations.
Problem: Matilda has a handful of quarters and dimes, with a total value of $8.55. The number of quarters is more than twice the number of dimes. How many dimes and how many quarters does she have?
- Read the problem. A table will help organize the information.
- Identify what to find: the number of dimes and the number of quarters.
- Name the unknowns. Let the number of quarters and the number of dimes. Organize the data into a table:
| Type | Number | Value ($) | Total Value ($) |
|---|---|---|---|
| Quarters | 0.25 | 0.25q | |
| Dimes | 0.10 | 0.10d | |
| Total | 8.55 |
-
Translate into a system of equations.
- The "Total Value" column gives the first equation:
- The relationship between the quantities (quarters is more than twice dimes) gives the second equation:
The system of equations is:
-
Solve the system using the substitution method. Substitute for in the first equation:
Distribute the 0.25:
Combine like terms:
Subtract 0.75 from both sides:
Divide by 0.60:
Substitute into the second equation to find :
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Check the result. quarters at $0.25 each is $7.25. dimes at $0.10 each is $1.30. checkmark
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Answer the question. Matilda has dimes and quarters.
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Intermediate Algebra @ OpenStax
Ch.4 Systems of Linear Equations - Intermediate Algebra @ OpenStax
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Food and Drink Mixture Applications
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Components of a Mixture System Setup
A manufacturing supervisor is blending two different grades of metal alloys for a specific production run. Arrange the following steps in the correct order to set up a system of equations that models this mixture application.
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Learn After
A retail supervisor is training a new employee to use a system of equations to reconcile a cash drawer containing only quarters () and dimes (). Match each verbal description of the problem's components with its correct mathematical representation.
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A treasury assistant is reconciling a donation box that contains only quarters () and dimes (). True or False: In the system of equations used to solve this mixture problem, the individual monetary values of the coins (such as {}0.25 for quarters and {}0.10 for dimes) are used as the coefficients for the variables in the equation representing the total dollar amount.
Understanding Coefficients in Coin Value Equations