What is the value of the smaller number if the difference between two numbers is 25 and the smaller number is 1/6th of the larger number?

Let’s denote the larger number as x and the smaller number as y.

According to the problem, we have two pieces of information:

• The difference between the two numbers: x – y = 25
• The smaller number is 1/6th of the larger number: y = rac{1}{6}x

We can substitute the second equation into the first one:

x - rac{1}{6}x = 25

This simplifies to:

rac{6}{6}x - rac{1}{6}x = 25

rac{5}{6}x = 25

To solve for x, multiply both sides by 6/5:

x = 25 * rac{6}{5} = 30

Now that we have the value of x, we can find y:

y = rac{1}{6}x = rac{1}{6} * 30 = 5

Thus, the value of the smaller number is 5.