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?

Hi admin, you made a small mistake

Difference means subtract.

Let x be the little one and y be the big one

y-x=25 (1)

y/6=x ==> y=6x (2)

sub (2) into (1)

6x-x=25

5x=25

x=5

y=6*5=30

$$\underset{\,\,\,\,{\textcolor[rgb]{0.66,0.66,0.66}{\rightarrow {\mathtt{x, y}}}}}{{solve}}{\left(\begin{array}{l}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{y}}={\mathtt{25}}\\ {\mathtt{x}}=\left({\frac{{\mathtt{1}}}{{\mathtt{6}}}}\right){\mathtt{\,\times\,}}{\mathtt{y}}\end{array}\right)} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\frac{{\mathtt{25}}}{{\mathtt{7}}}}\\ {\mathtt{y}} = {\frac{{\mathtt{150}}}{{\mathtt{7}}}}\\ \end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{3.571\: \!428\: \!571\: \!428\: \!571\: \!4}}\\ {\mathtt{y}} = {\mathtt{21.428\: \!571\: \!428\: \!571\: \!428\: \!6}}\\ \end{array} \right\}$$