### Take a number x, and multiply it with 5. Take the cube of the resulting number. What is the ratio of this number to the cube of the original number?

125:1

Step by Step Explanation:
1. If we multiply the number x with 5, the resulting number is 5x.
2. The cube of the resulting number 5x = (5x)3
= 125x3
3. The original number is x.
Cube of the original number = x3.
4. The ratio of the new number to the original number =
 New number Original number

=
 125x3 x3

=
 125 1

5. Therefore, the ratio of the new number to the cube of the original number is 125:1.