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 Alex and gave him 1/4 of his remaining marbles plus 5. Just before arriving at the tournament, he met Emily 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?

Answer 1

Let's use the same approach of backward reasoning to arrive at the answer:

When Andy arrived at the tournament, he had 2 marbles left. Just before that, he gave 1/2 of his remaining marbles to Emily. So, if he had 2 marbles left after giving half to Emily, he must have had 4 marbles before giving half to Emily.

Before meeting Emily, Andy gave 1/4 of his remaining marbles plus 5 to Alex. So, if he had 4 marbles left after giving 1/4 to Alex, he must have had (4 - 5) / (1/4) = 16 marbles before giving 1/4 to Alex.

Before meeting Alex, Andy gave Bob 1/2 of his marbles plus 2. So, if he had 16 marbles left after giving 1/2 plus 2 to Bob, he must have had (16 - 2) x 2 = 28 marbles before giving 1/2 plus 2 to Bob.

Therefore, Andy started with 28 marbles.

Answer 2

Good job! That's the correct answer. Using backward reasoning can be a helpful strategy to solve problems like this one.