Question

A Roman statue is three times as old as a Florentine statue. One hundred years from now the Roman statue will be twice as old as the Florentine statue. How old is the Roman statue?

Answer 1

The Roman statue is 300 years old.

Step-by-step explanation:

To solve this problem, we can start by setting up equations using the information given. Let's assume that the age of the Florentine statue is x years. According to the problem, the Roman statue is three times as old, so its age can be represented as 3x years.

After 100 years, the Roman statue will be twice as old as the Florentine statue. This can be expressed as:

3x + 100 = 2(x + 100)

Now, we can solve this equation for x to find the age of the Florentine statue:

3x + 100 = 2x + 200

x = 100

Therefore, the Florentine statue is 100 years old. To find the age of the Roman statue, we can substitute this value back into the equation:

3(100) = 300

Therefore, the Roman statue is 300 years old.

Answer 2

Let's assume the age of the Florentine statue is represented by 'x' years.

According to the given information, the Roman statue is three times as old as the Florentine statue. So, the age of the Roman statue can be represented as '3x' years.

We are also told that one hundred years from now, the Roman statue will be twice as old as the Florentine statue. So, we can set up the following equation:

(3x + 100) = 2(x + 100)

Let's solve this equation to find the age of the Roman statue:

3x + 100 = 2x + 200

3x - 2x = 200 - 100

x = 100

Therefore, the age of the Florentine statue is 100 years.

To find the age of the Roman statue, we can substitute this value back into the equation:

Roman statue's age = 3x = 3 * 100 = 300 years

So, the Roman statue is 300 years old.

I hope this helps! Let me know if you have any other questions.