Sum of the three numbers word problem

The sum of three numbers is 81. The first number is half the second, and the third number is three times the second one. What is the value of the first number?

x = second number
x/2 = first number {first number is half the second}
3x = third number {third number is three times the second} 


x + x/2 + 3x = 81 {the sum of the three numbers is 81}
2x + x + 6x = 162 {multiplied entire equation by 2 to eliminate fraction}
9x = 162 {combined like terms}
x = 18 {divided each side by 9}
x/2 = 9 {substituted 18, in for x, into x/2} 

the first number is 9

- Algebra House