Apply the seven-step problem-solving strategy and the total-value model to a stamp mixture problem where each stamp type has a decimal value and the relationship between the two stamp counts involves both multiplication and addition.

Problem: Monica paid $8.36 for stamps. The number of 41-cent stamps was four more than twice the number of two-cent stamps. How many 41-cent stamps and how many two-cent stamps did Monica buy?

1. Read the problem and identify the types involved: 41-cent stamps (worth $0.41 each) and two-cent stamps (worth $0.02 each). The total value of all stamps is $8.36.
2. Identify what to find: the number of 41-cent stamps and the number of two-cent stamps.
3. Name the unknowns using a single variable. Let $x$ = the number of two-cent stamps. The phrase "four more than twice" combines multiplication by $2$ with adding $4$, so the number of 41-cent stamps is $2x + 4$. Organize in a table:

Type	Number	Value ($)	Total Value ($)
41-cent stamps	$2x + 4$	0.41	$0.41(2x + 4)$
2-cent stamps	$x$	0.02	$0.02x$
			8.36

4. Translate into an equation by adding the total values and setting the sum equal to the overall total:

$0.41(2x + 4) + 0.02x = 8.36$

5. Solve the equation:

• Distribute $0.41$: $0.82x + 1.64 + 0.02x = 8.36$
• Combine like terms: $0.84x + 1.64 = 8.36$
• Subtract $1.64$ from both sides: $0.84x = 6.72$
• Divide both sides by $0.84$: $x = 8$

Find the number of 41-cent stamps: $2(8) + 4 = 16 + 4 = 20$.

6. Check: $8(0.02) + 20(0.41) \stackrel{?}{=} 8.36$ → $0.16 + 8.20 = 8.36$ $\checkmark$
7. Answer: Monica bought eight two-cent stamps and twenty 41-cent stamps.

This example demonstrates that the total-value model applies to stamps just as it does to coins and tickets — each stamp type has a fixed per-unit value, and the product of count times value gives the total value for that type. Here the relationship "four more than twice" translates to $2x + 4$, and distributing the decimal value $0.41$ across $2x + 4$ produces $0.82x + 1.64$. After combining $0.82x + 0.02x$ into $0.84x$, the final division step $6.72 \div 0.84$ requires careful decimal arithmetic — a skill reinforced by working with non-standard item values like $0.41$ rather than the rounder values typical of coins.