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?

[tex]x > y\\\\x-y=25\\\\y=\frac{1}{6}x-substitute:\\\\x-\frac{1}{6}x=25\\\\\frac{5}{6}x=25\ \ \ \ /\cdot\frac{6}{5}\\\\x=25\cdot\frac{6}{5}\\\\x=5\cdot6\\\\x=30\\\\30-y=25\to y=5\\\\Answer:The\ smaller\ number\ is\ 5.[/tex]

x - larger numbery - smaller number[tex]x-y=25\\
y=\frac{x}{6}\\\\
x=y+25\\
6y=x\\
\\6y=y+25\\
5y=25\\
y=5
[/tex]