Learn Before
Example: Solving a Stamp Mixture Problem with 49-Cent and 35-Cent Stamps (Multiplication and Subtraction)
Apply the seven-step problem-solving strategy and the total-value model to a stamp mixture problem where the relationship between the two stamp counts involves both multiplication and subtraction.
Problem: Danny paid $15.75 for stamps. The number of 49-cent stamps was five less than three times the number of 35-cent stamps. How many 49-cent stamps and how many 35-cent stamps did Danny buy?
- Read the problem and identify the types involved: 49-cent stamps (worth $0.49 each) and 35-cent stamps (worth $0.35 each). The total value of all stamps is $15.75.
- Identify what to find: the number of 49-cent stamps and the number of 35-cent stamps.
- Name the unknowns using a single variable. Let = the number of 35-cent stamps. The phrase "five less than three times" combines multiplication by with subtracting , so the number of 49-cent stamps is .
Organize in a table:
| Type | Number | Value (in dollars) | Total Value (in dollars) |
|---|---|---|---|
| 49-cent stamps | 0.49 | ||
| 35-cent stamps | 0.35 | 0.35x | |
| Total | 15.75 |
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Translate into an equation by adding the total values and setting the sum equal to the overall total:
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Solve the equation:
- Distribute 0.49:
- Combine like terms:
- Add 2.45 to both sides:
- Divide both sides by 1.82:
Find the number of 49-cent stamps: .
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Check: Does ? checkmark
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Answer: Danny bought 10 thirty-five-cent stamps and 25 forty-nine-cent stamps.
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Intermediate Algebra @ OpenStax
Ch.2 Solving Linear Equations - Intermediate Algebra @ OpenStax
Algebra
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The Components of the Total-Value Model
A corporate logistics coordinator is analyzing the costs of two different postage stamp denominations used for a mass mailing campaign. To correctly apply the total-value model and determine the quantity of each stamp type purchased, arrange the following algebraic steps in the correct sequence.
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Unified Cost Modeling in Operations
Example: Solving a Stamp Mixture Problem with 49-Cent and 35-Cent Stamps (Multiplication and Subtraction)
Example: Solving a Stamp Mixture Problem with 49-Cent and 20-Cent Stamps
Learn After
You are an office manager reconciling the monthly postage inventory, which consists of 49-cent and 35-cent stamps. To determine the exact quantities used, you must first translate the problem into algebraic terms. You recall from the inventory log that 'the number of 49-cent stamps was five less than three times the number of 35-cent stamps.' If you assign the variable to represent the number of 35-cent stamps, which of the following expressions correctly represents the number of 49-cent stamps?
An office coordinator is reconciling postage expenses for a bulk mailing project. They need to determine how many 49-cent and 35-cent stamps were purchased for a total of 15.75. Based on the standard problem-solving strategy for mixture problems, arrange the following steps in the correct order to solve this scenario.
An office manager is reconciling a receipt for a mixture of 49-cent and 35-cent stamps with a total cost of {}15.75. The inventory log notes that the number of 49-cent stamps was 'five less than three times' the number of 35-cent stamps (x). To model this, the manager uses the equation:{}0.49(3x - 5) + 0.35x = 15.75$. Match each component of the equation to its corresponding real-world meaning.
Postage Inventory Reconciliation
When using the total-value model to reconcile postage expenses, the 'Total Value' of a specific type of stamp is calculated by multiplying the number of stamps by the ____ of each individual stamp.
In an office shipping department, an administrative assistant is setting up a total-value equation to reconcile a postage purchase of 49-cent and 35-cent stamps. The assistant notes that the number of 49-cent stamps was 'five less than three times' the number of 35-cent stamps ().
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Translating the Total-Value Table into an Equation