Find the smaller number

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}

the smaller number is 5

- Algebra House