Using the proportion (2 balls / $7) = (20 balls / x dollars), we can solve for x:
2 * x = 7 * 20
Now, let's do the math:
2x = 140
To find the value of x, we divide both sides of the equation by 2:
x = 70
So, it will cost $70 to buy 20 balls of yarn. The answer is option C.