Andy was on his way to a marble tournament when he met Bob. Andy’s bag of marbles was heavy, so he gave Bob one-half of his marbles plus 2. Then he met Alex and gave him one-fourth of his remaining marbles plus 5. Just before arriving at the tournament, he met Emily and gave her one-half of the marbles he had left. When he got to the tournament, he had 2 marbles left. How many marbles did he start with?
7 comments:
I would go backwards...and if that gets too complicated I would start at a number below 25 and guess and check!
One way to do it is to 1st guess a number. Start at 25 or lower. Then subtract half. Then subtract 1/4 of the remaining number of marbles. Then, subtract half of the remaining marbles. This should give you 2. The number of marbles in the begginning is the number that equals 2 after doing all these steps.
This IS an excellent problem to try to solve working backwards, Yvonne. Great idea!
i was alsi going to say that you need to work backwards. but you have to make sure you remember that when it says 1/2, it means 1/2 of the marbles. not half a marble. that would totally confuse me.
What I did was also work backwards. I started with 2 then I did 2 plus 2 because 2+x=4 X=4 that is half. Then he gave 5 so +5. and then the total of this is 9. then you do plus 1/4 of the marbles then +2 then plus 1/2 of the reeeeest of the marbles
Good comments!
Working backwards is an excellent strategy for this problem. Then once you think you have it, check it going forwards to make sure it works.
Working backwards, the opposite of one-half would be times 2. The opposite of plus two would be minus two and so forth.
So if he started with 28 marbles and gave Bob half plus two then he would give Bob 16 and he would have 12 left. Then if he gave Alex one-fourth plus 5, he would have given Alex 8 which would have left him 4, before he met Emily. When he gave Emily half, he gave her 2, which would have left him with two marbles, so if you got 28 by working backwards, then it checks!
So it is true he started with 28 marbles.
I would just guess and check, it would be easier than working backwards.
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