Final answer:
The mystery number in the contest question where sixteen more than 2/3 of the mystery number equals twice the mystery number is 12 (option C).
Step-by-step explanation:
To solve the mystery number contest problem, which is to find a number such that sixteen more than 2/3 of it equals twice the number itself, we set up an equation to represent the situation:
16 + 2/3x = 2x
To find the value of x, we first subtract 2/3x from both sides of the equation to get:
16 = 2x - 2/3x
We then find a common denominator for the x terms:
16 = (6/3)x - (2/3)x
This simplifies to:
16 = (4/3)x
Next, we multiply both sides by the reciprocal of the fraction to isolate x:
16 * (3/4) = x
This ends up giving us:
12 = x
Thus, the mystery number is 12, which is option C).