1Cademy - Example: Solving a Stamp Mixture Problem with 49-Cent and 35-Cent Stamps

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Problem-Solving Strategy for Coin Word Problems

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Example: Solving a 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 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 $x$ = the number of 35-cent stamps. The phrase "five less than three times" combines multiplication by $3$ with subtracting $5$ , so the number of 49-cent stamps is $3x - 5$ . Organize in a table:

Type	Number	Value ($)	Total Value ($)
49-cent stamps	$3x - 5$	$0.49$	$0.49(3x - 5)$
35-cent stamps	$x$	$0.35$	$0.35x$
			$15.75$

Translate into an equation by adding the total values and setting the sum equal to the overall total: $0.49(3x - 5) + 0.35x = 15.75$
Solve the equation:

Distribute $0.49$ : $1.47x - 2.45 + 0.35x = 15.75$
Combine like terms: $1.82x - 2.45 = 15.75$
Add $2.45$ to both sides: $1.82x = 18.2$
Divide both sides by $1.82$ : $x = 10$

Find the number of 49-cent stamps: $3(10) - 5 = 30 - 5 = 25$ .

Check: Does $10(0.35) + 25(0.49) = 15.75$ ? $3.50 + 12.25 = 15.75$ $15.75 = 15.75 \checkmark$
Answer: Danny bought $10$ 35-cent stamps and $25$ 49-cent stamps.

Updated 2026-04-22

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OpenStax Intermediate Algebra

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