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Question 1197358: If Carmen distributes the pieces of a cake to 7 classmates, she has 2 left over, but if she distributes them to her 6 brothers, she does not have any left over. What is the minimum number of pieces that the cake has?
Answer by ikleyn(52824)   (Show Source):
You can put this solution on YOUR website! .
If Carmen distributes the pieces of a cake to 7 classmates, she has 2 left over,
but if she distributes them to her 6 brothers, she does not have any left over.
What is the minimum number of pieces that the cake has?
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They want you find the minimum positive integer number, multiple of 6,
which gives the remainder 2 when divided by 7.
The shortest way to get the solution/answer is to apply the "trial and error" method
6 gives the remainder 6 when divided by 7. So 6 is not the solution.
12 gives the remainder 5 when divided by 7. So 12 is not the solution.
18 gives the remainder 4 when divided by 7. So 18 is not the solution.
24 gives the remainder 3 when divided by 7. So 24 is not the solution.
30 gives the remainder 2 when divided by 7. So 30 is the solution.
ANSWER. The minimum number of pieces Carmen has is 30.
Solved.
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