Final answer:
The number that is three times the difference between twenty and the number itself is 15, as derived from the algebraic equation x = 3(20 - x).
Step-by-step explanation:
The question asks to find a number that is three times the difference between twenty and the number itself. To solve this, we set up an equation where the number is represented by 'x'. Therefore, the equation is x = 3(20 - x).
To find the value of x, we first distribute the 3 through the parenthesis, which gives us x = 60 - 3x. Then, to get all the x's on one side of the equation, we add 3x to both sides: 4x = 60. Lastly, we divide both sides of the equation by 4 to isolate x, which gives us x = 15. Hence, the number that satisfies the given condition is 15.