Final answer:
Lucy ends up with 11 balls after giving 10 to Alex, who then divides them by 8 and returns the whole number part back to Lucy, which is 1 ball.
Step-by-step explanation:
If Lucy had 20 balls and gives Alex 10 balls, then Alex divided those 10 balls by 8 and gave the result back to Lucy. First, we calculate the division that Alex did, which is 10 divided by 8. This does not result in a whole number, so Alex can't give exactly 10/8 balls to Lucy; the division results in a number with a decimal. However, assuming Alex gives Lucy the whole part of the division, she would give Lucy 1 ball back since 10 divided by 8 equals 1 with a remainder.
Next, we add the 1 ball that Lucy receives back from Alex to the remaining 10 balls that she did not give away. Therefore, Lucy has 10 + 1 = 11 balls in the end. So, the correct answer is not listed among the choices provided (A. 5, B. 6, C. 7, D. 8).