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Example: Solving a Stamp Mixture Problem with 49-Cent and 20-Cent Stamps
Apply the seven-step problem-solving strategy and the total-value model to a stamp mixture problem to find the numbers of two different stamps when their total cost is known.
Problem: Kailee paid $14.74 for stamps. The number of 49-cent stamps was four less than three times the number of 20-cent stamps. How many 49-cent stamps and how many 20-cent stamps did Kailee buy?
- Read the problem and identify the types involved: 49-cent stamps (worth $0.49 each) and 20-cent stamps (worth $0.20 each). The total value is $14.74.
- Identify what to find: the number of 49-cent stamps and the number of 20-cent stamps.
- Name the unknowns using a single variable. Let = the number of 20-cent stamps. The phrase "four less than three times" translates to . Therefore, the number of 49-cent stamps is .
- Translate into an equation:
- Solve the equation:
- Distribute 0.49:
- Combine like terms:
- Add 1.96 to both sides:
- Divide both sides by 1.67: Find the number of 49-cent stamps: .
- Check: Does ? 14.74 = 14.74 checkmark
- Answer: Kailee bought 10 20-cent stamps and 26 49-cent stamps.
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Intermediate Algebra @ OpenStax
Ch.2 Solving Linear Equations - Intermediate Algebra @ OpenStax
Algebra
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Example: Solving a Stamp Mixture Problem with 49-Cent and 20-Cent Stamps
Learn After
An administrative assistant at a community college is auditing a mailing expense for a department. The total spent was {}14.74 for a combination of 49-cent stamps and 20-cent stamps. The record indicates that the number of 49-cent stamps purchased was 'four less than three times the number of 20-cent stamps.' If represents the number of 20-cent stamps, which algebraic expression correctly represents the number of 49-cent stamps?
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An office manager is reconciling a receipt for {}14.74 spent on two types of postage: 20-cent stamps and 49-cent stamps. The records indicate that the number of 49-cent stamps purchased was four less than three times the number of 20-cent stamps. To model this situation algebraically using the total-value method, match each description with its correct algebraic representation.
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