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 $8.55. The number of quarters is more than twice the number of dimes. How many dimes and how many quarters does she have?
- Read the problem. A table will help organize the information.
- Identify what to find: the number of dimes and the number of quarters.
- Name the unknowns. Let be the number of quarters and be the number of dimes. Organize the data into a table:
| Type | Number | Value ($) | 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 :
- Check the result.
- quarters at $0.25 each is $7.25.
- dimes at $0.10 each is $1.30.
- checkmark
- Answer the question. Matilda has dimes and quarters.
0
1
Tags
OpenStax
Intermediate Algebra @ OpenStax
Ch.4 Systems of Linear Equations - Intermediate Algebra @ OpenStax
Algebra
Related
Solving a Science Center Ticket Mixture Application
Solving a Coin Mixture Problem Using a System of Equations
Solving a Quarters and Dimes Mixture Problem Using a System of Equations
Solving a Nickels and Quarters Mixture Problem Using a System of Equations
Solving a Laboratory Acid Mixture Problem Using a System of Equations
Solving a Sulfuric Acid Mixture Application Using a System of Equations
Solving a Hydrochloric Acid Mixture Problem Using a System of Equations
Solving a Trail Mix Mixture Problem Using a System of Equations
Solving a Nut Mix Application Using a System of Equations
Solving a Recipe Mixture Application Using a System of Equations
Setting Up an Interest Application Using a System of Equations
Solving an Investment Fund Interest Application Using a System of Equations
Solving a Savings and Stock Interest Application Using a System of Equations
Solving a Dual Stock Interest Application Using a System of Equations
Solving a Student Loan Interest Application Using a System of Equations
Solving a Dual Student Loan Interest Application Using a System of Equations
Food and Drink Mixture Applications
An inventory specialist is mixing two types of bulk products for a shipment. Match each part of the 'System of Equations' model with the specific relationship or component it represents in a mixture application.
As a production supervisor, you are setting up a system of equations to determine the exact amounts of two different grades of raw materials needed for a manufacturing batch. When using the system of equations method for this mixture application, how do you initially represent the unknown amounts of the two materials?
A procurement officer is blending two different grades of metal alloys for a large-scale construction project. To model this mixture scenario using a system of equations, the officer must establish two separate equations: one representing the total physical quantity (such as the total weight) of the alloys and a second representing the total monetary or quantitative worth (the total value) of those alloys.
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.
An inventory specialist is blending two different grades of metal alloys to meet a manufacturing specification. To find the required amount of each alloy, the specialist sets up a system of equations with two separate variables, and . The first equation is created from the total physical count or weight, and the second equation is created from the total ____ of the components in the mixture.
Formulating a Mixture System of Equations
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.
A fundraising coordinator is reconciling a donation jar that contains only quarters and dimes. To determine the exact number of each coin using a system of linear equations, the coordinator follows a standard seven-step problem-solving strategy. Arrange the following steps in the correct order to solve this coin mixture problem.
A treasury assistant for a non-profit organization is reconciling a donation box that contains only quarters () and dimes (). To calculate the total amount of money collected, the assistant uses the mathematical expression . In this expression, what does the specific term {}0.25q represent?
A retail supervisor is training a new employee to reconcile a petty cash drawer containing only quarters () and dimes () with a total value of 8.55 dollars. The supervisor explains that the total monetary value is represented by the equation ____ . Fill in the blank with the correct mathematical term that represents the total value of the dimes.
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
Reconciling a Recreation Center Cash Box Using a System of Equations