What is the fewest number of cubes in these cups to make these outcomes possible? How did you know this is the fewest amount? Can you find the larger amount?

Question

There are three cups with the same amount of cubes in each one. A person removes two cubes at a time from the first cup and had one cube left over. Then the person decides to remove three cubes at a time from the second cup and this time had two cubes left over. Lastly, the person decides to remove 5 cubes at a time and now has 3 left over. What is the fewest number of cubes in these cups to make these outcomes possible? How did you know this is the fewest amount? Can you find the larger amount?

Answer 1

First cup implies it is an odd number

 

Second cup implies that the remainder is 2 when divided by 3.

 

Third cup implies that remainder is 3 when dividing by 5.

 

23 is the first odd number that satisfies these conditions.

 

53 is the next odd number that satisfies these conditions.