5th grade story problem

cpeterson

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Dec 11, 2014
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If you have a 3-cup container and a 5-cup container, how can you measure exactly 1 cup?
 
If you have a 3-cup container and a 5-cup container, how can you measure exactly 1 cup?
I don't think there's any formula for this sort of exercise. You just need to fiddle around with the measurements until you note a sequence of pourings and dumpings which will lead to the amount you want. For instance, if you fill the 3-cup and pour this into the 5-cup, how much empty space is left in each of the containers? Can this result lead anywhere useful? And so forth.

Have fun! ;)
 
I don't think there's any formula for this sort of exercise. You just need to fiddle around with the measurements until you note a sequence of pourings and dumpings which will lead to the amount you want. For instance, if you fill the 3-cup and pour this into the 5-cup, how much empty space is left in each of the containers? Can this result lead anywhere useful? And so forth.

Have fun! ;)
How about this- 5x+ 3y= 1. Euclidean algorithm- 3 divides into 5 once with remainder 2: 5- 3= 2. 2 divides into 3 with remainder 1: 3- 2= 1. Replace that "2" in the second equaton by 5- 3: 3- (5- 3)= 2(3)- 5= 1.

Fill the 3 cup measure. Pour that into the 5 cup measure. Fill the 3 cup measure with water. pour that into the 5 cup measure until the 5 cup measure until it is full. That leaves 1 cup of water in the three cup measure.
 
How about this- 5x+ 3y= 1. Euclidean algorithm- 3 divides into 5 once with remainder 2: 5- 3= 2. 2 divides into 3 with remainder 1: 3- 2= 1. Replace that "2" in the second equaton by 5- 3: 3- (5- 3)= 2(3)- 5= 1.

Fill the 3 cup measure. Pour that into the 5 cup measure. Fill the 3 cup measure with water. pour that into the 5 cup measure until the 5 cup measure until it is full. That leaves 1 cup of water in the three cup measure.

but not for any 5th graders I know.
 
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