Answer: The number is 84
Step-by-step explanation: First of all, let the number be x. The third part of the number can be written as x/3. Twice the sum of that plus five can be written as 2(x/3) plus 5.
2(x/3) can be re-written as 2x/3. Hence we have (2x/3) + 5 on one side of the expression.
Also three quarters of that number can be written as 3/4 times x which can also be written as 3x/4. Three quarters of that number minus two can now be written as (3x/4) - 2 on the other side of the expression
Hence we now have,
(2x/3) + 5 = (3x/4) - 2
We need to have a common denominator for each side of the equation, hence
(2x + 15)/3 = (3x - 8)/4
By cross multiplication we now have
4(2x + 15) = 3(3x - 8)
By expanding the brackets we now have
8x + 60 = 9x - 24
By collecting like terms we have
60 + 24 = 9x - 8x
84 = x