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?

x = larger number

x/6 = smaller number {the smaller number is 1/6th the larger number}

x - x/6 = 25 {difference of the two numbers is 25}

6x - x = 150 {multiplied entire equation by 6 to eliminate fraction}

5x = 150 {combined like terms}

x = 30 {divided each side by 5}

x/6 = 5 {substituted 30, in for x, into x/6}

x/6 = smaller number {the smaller number is 1/6th the larger number}

x - x/6 = 25 {difference of the two numbers is 25}

6x - x = 150 {multiplied entire equation by 6 to eliminate fraction}

5x = 150 {combined like terms}

x = 30 {divided each side by 5}

x/6 = 5 {substituted 30, in for x, into x/6}

**the smaller number is 5**

*- Algebra House*