Problem 7 · Track two piles backward · 5 points
Made by AI and not reviewed by a real person.
Ada and Bo play three rounds with marbles: first Ada gives Bo as many as Bo already has, then Bo gives Ada as many as Ada now has, and finally Ada gives Bo as many as Bo now has. If they end with 24 marbles each, how many did Ada start with?
- 24
- 36
- 15
- 33
- 18
Show a hint
- No marbles are added or lost. Think about what each gift does to the receiver’s pile.
- Start with the final gift: Bo had half as many marbles just before it as he had afterward. Use the total to find Ada’s pile at that moment, then keep working toward the start.
Show the answer and solution
Answer: D — 33
Together they always have 48 marbles. Just before the final gift, Bo had 12 and Ada had 36. Just before the middle gift, Ada had 18 and Bo had 30; just before the first gift, Bo had 15 and Ada had 33. So Ada started with 33. The tempting answer 36 is what Ada had just before the final gift, not at the start.