Final answer:
The two numbers that are twice as far from 25 as they are from 64 are approximately 29.67 and 153. The distance equation to calculate these numbers is |x - 25| = 2 * |x - 64| and two separate cases are considered due to the absolute values.
Step-by-step explanation:
The question is asking to find two numbers that are twice as far from 25 as they are from 64. Let's denote one of the numbers as x.
The distance from x to 25 can be represented as |x - 25|, and the distance from x to 64 is |x - 64|. Stating that x is twice as far from 25 as it is from 64 can be translated to an equation: |x - 25| = 2 * |x - 64|.
We have to consider two cases because of the absolute value:
- When x is between 25 and 64, we solve (x - 25) = 2*(64 - x). This gives us x = 89/3, which is approximately 29.67.
- When x is outside the interval between 25 and 64, we solve (x - 25) = 2*(x - 64), which gives us x = 153.
So the two numbers that are twice as far from 25 as they are from 64 are approximately 29.67 and 153.