7. A person spends $\$ 300,000$ on a total of 3 properties. The first property's value is the sum of the other two properties. The second property is twice the value of the third property. How much does each property cost?
Solution
Step 1 ：Let's denote the cost of the first property as x, the cost of the second property as y, and the cost of the third property as z.
Step 2 ：From the problem, we know that the total cost of all properties is $300,000, so we can write this as an equation: \(x + y + z = 300,000\).
Step 3 ：We also know that the first property's value is the sum of the other two properties, so we can write this as another equation: \(x = y + z\).
Step 4 ：Finally, we know that the second property is twice the value of the third property, so we can write this as a third equation: \(y = 2z\).
Step 5 ：We can solve this system of equations to find the values of x, y, and z.
Step 6 ：The solution to the system of equations gives the cost of each property. The first property costs $150,000, the second property costs $100,000, and the third property costs $50,000.
Step 7 ：This is consistent with the conditions given in the problem: the first property's value is the sum of the other two properties, and the second property is twice the value of the third property.
Step 8 ：Final Answer: The first property costs \(\boxed{\$150,000}\), the second property costs \(\boxed{\$100,000}\), and the third property costs \(\boxed{\$50,000}\).
