Question 651441: Have you Lost Your Marbles?
Andy was on his way to a marble tournament when he met Bob. Andy's bag of marbles was heavy, so he gave Bob 1/2 of his marbles plus 2. Then he met Cindy and gave her 1/4 of his remaining marbles plus 5. Just before arriving at the tournament, he met Denise and gave her 1/2 of the marbles he had left. When he got to the tournament, he had 2 marbles left. How many marbles did he start with?
I am a 6th Grade student. I am having difficulties approaching this and putting it into an equation. I also must understand the thought process. Can you please help me!!
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! Let N = the original number of marbles
Andy gives Bob 1/2 his marbles plus 2, which is N/2 + 2, so Andy has:
N - (N/2 + 2) = N/2 - 2 marbles left
Andy gives Cindy 1/4 of the remaining marbles plus 5, which is
1/4(N/2-2) + 5 = N/8 + 9/2
So Andy has N/2 - 2 - (N/8+9/2) = 3N/8 - 13/2 left
Andy gives Denise half of the remaining marbles, which is 1/2(3N/8 - 13/2), and this number is equal to 2:
2 = 3N/16 - 13/4
Solve for N:
32 = 3N - 52
3N = 84
N = 28
So Andy started with 28 marbles
Check:
After Bob, he has 28 - (14+2) = 12 left
After Cindy, he has 12 - (12/4+5) = 4 left
After Denise, he has 4 - 4/2 = 2 left
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