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Example: Another Stamp Mixture Problem with 49-Cent and 35-Cent Stamps
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 addition.
Problem: Eric paid $19.88 for stamps. The number of 49-cent stamps was eight more than twice the number of 35-cent stamps. How many 49-cent stamps and how many 35-cent stamps did Eric 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 $19.88.
- 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 "eight more than twice" translates to . Therefore, the number of 49-cent stamps is .
- Translate into an equation: Multiply each count by its respective value, then sum them to equal the total value:
- Solve the equation:
- Distribute :
- Combine like terms:
- Subtract from both sides:
- Divide both sides by :
Find the number of 49-cent stamps: . 6. Check: Does ? 7. Answer: Eric bought 35-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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Learn After
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