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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 :
- Combine like terms:
- Add to both sides:
- Divide both sides by :
Find the number of 49-cent stamps: . 6. Check: Does ? 7. Answer: Kailee bought 20-cent stamps and 49-cent stamps.
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Intermediate Algebra @ OpenStax
Ch.2 Solving Linear Equations - Intermediate Algebra @ OpenStax
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Example: Solving a Coin Mixture Problem with Dimes and Nickels
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Example: Solving a Stamp Mixture Problem with 49-Cent and 35-Cent Stamps
Example: Another Stamp Mixture Problem with 49-Cent and 35-Cent Stamps
Example: Solving a Stamp Mixture Problem with 49-Cent and 20-Cent Stamps