twice the sum of the third part of a number plus 5 is equal to three quarters of that number minus two. what is the number?

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