Final answer:
To find the cost of each property, we use the equations 3x (first property) = 2x (second property) + x (third property) and solve for x. After realizing 6x = $300,000, we determine x to be $50,000, giving us the costs of $150,000, $100,000, and $50,000 for the first, second, and third properties respectively.
Step-by-step explanation:
To solve the problem, we need to set up equations based on the given information. The total amount spent on 3 properties is $300,000. Let's say the cost of the third property is x. Therefore, the cost of the second property, which is twice the value of the third property, would be 2x. The first property's value is the sum of the other two properties, so its cost is x + 2x, which simplifies to 3x.
Now we have three properties costing 3x, 2x, and x respectively, and since the total cost is $300,000, we can write the equation:
3x + 2x + x = $300,000
Combining like terms gives:
6x = $300,000
Dividing both sides of the equation by 6 gives:
x = $50,000
This is the cost of the third property. Following from this, the second property costs 2x, which is:
2 * $50,000 = $100,000
And the first property, costing 3x, is:
3 * $50,000 = $150,000
So the cost of each property is:
- First property: $150,000
- Second property: $100,000
- Third property: $50,000