The difference between two numbers is 25. The smaller number is 1/6th of the larger number. What is the value of the smaller number

Let the smaller number be s. Let the larger number be l. We're given two equations:

l - s = 25

s = l/6

Plug in equation (2) into equation (1):
l - l/6 = 25

Multiply each side of the equation by 6 to remove the fraction:
6l - l = 150

To solve for l, we type this equation into our search engine and we get:
l = 30

To solve for s, we plug in l = 30 into equation (2) above:
s = 30/6
s = 5

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