Marco paid $9{,}000 for 2 used automobiles. The amount he paid for the more expensive automobiles was $300 less than...

1. Translate the problem requirements: Marco bought 2 cars for a total of $9,000. The more expensive car cost $300 less than 3 times what the less expensive car cost. We need to find the price of the more expensive car.
2. Set up variables for the two car prices: Define variables for the less expensive and more expensive car prices based on the given relationship.
3. Create equations from the given conditions: Use the total cost and the relationship between the two prices to form a system of equations.
4. Solve for the car prices: Substitute one equation into the other to find the price of each car, focusing on the more expensive one.

Execution of Strategic Approach

1. Translate the problem requirements

Let's break down what we know in plain English:

• Marco bought 2 used cars
• He paid a total of $9,000 for both cars combined
• One car was more expensive than the other
• The more expensive car cost $300 less than 3 times what the less expensive car cost
• We need to find how much he paid for the more expensive car

Think of it this way: if the cheaper car cost $2,000, then 3 times that would be $6,000, and $300 less than that would be $5,700 for the expensive car. But we need to find the actual numbers that add up to $9,000 total.

Process Skill: TRANSLATE - Converting the word problem into mathematical relationships

2. Set up variables for the two car prices

Let's use simple letters to represent what we don't know:

• Let \(\mathrm{L}\) = the price Marco paid for the less expensive car
• Let \(\mathrm{M}\) = the price Marco paid for the more expensive car

Now we can express the relationship in plain English first: "The more expensive car costs $300 less than 3 times the less expensive car."

In mathematical terms: \(\mathrm{M} = 3\mathrm{L} - 300\)

3. Create equations from the given conditions

We have two key pieces of information that give us two equations:

Equation 1 (Total cost): The two cars together cost $9,000
\(\mathrm{L} + \mathrm{M} = 9000\)

Equation 2 (Relationship between prices): The more expensive car costs $300 less than 3 times the less expensive car
\(\mathrm{M} = 3\mathrm{L} - 300\)

These two equations contain all the information we need to solve for both car prices.

Process Skill: INTERPRET - Understanding the relationships and constraints

4. Solve for the car prices

Since we know that \(\mathrm{M} = 3\mathrm{L} - 300\), we can substitute this into our first equation:

\(\mathrm{L} + \mathrm{M} = 9000\)
\(\mathrm{L} + (3\mathrm{L} - 300) = 9000\)

Simplifying the left side:
\(\mathrm{L} + 3\mathrm{L} - 300 = 9000\)
\(4\mathrm{L} - 300 = 9000\)

Adding 300 to both sides:
\(4\mathrm{L} = 9300\)

Dividing by 4:
\(\mathrm{L} = 2325\)

So the less expensive car cost $2,325.

Now we can find the more expensive car's price:
\(\mathrm{M} = 3\mathrm{L} - 300\)
\(\mathrm{M} = 3(2325) - 300\)
\(\mathrm{M} = 6975 - 300\)
\(\mathrm{M} = 6675\)

Let's verify: $2,325 + $6,675 = $9,000 ✓

5. Final Answer

Marco paid $6,675 for the more expensive automobile.

Looking at our answer choices, this matches choice (D) $6,675.

Verification:

• Less expensive car: $2,325
• More expensive car: $6,675
• Total: $2,325 + $6,675 = $9,000 ✓
• Relationship check: \(3 \times 2325 - 300 = 6975 - 300 = 6675\) ✓

The answer is (D) $6,675.