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Math!!!!!!!!! please help. im gonna go crazy. with this math homework?
okay heres the problem:
Sarah has between 50 and 100 pennies in her collection. When she divides them into groups of 2, of 3, or of 7, there is always one penny left. How many pennies does Sarah have in her collection?
IM SO CONFUSED PLEASE HELP ME.
and let me know what math strategy you used to solve it.
i need this done by tomorrow so please help me!!!
2 Answers
- np_rtLv 41 decade agoFavorite Answer
The number of pennies is of the form 2x+1, 3y+1, 7z+1 in order for it to leave 1 when you divide by 2, 3, and 7 respectively. Also, x, y, and z are positive integers.
All 3 of these numbers must be equal. So you have 2x = 3y, 2x = 7z. Since they are all positive integers, x must contains a factor of 3 and of 7.
So the number must be of the form, 2*3*7*k + 1 = 42k + 1. Substitute values for k in to get 43, 85, 127... The only value between 50 and 100 is 85.
- Anonymous1 decade ago
There is got to be a more elegant solution to this but here goes:
You always have one coin left over whenever you put them in the groups mentioned. So.... You know that the number minus 1 is divisible by 2, 3, and 7.
What's the smallest number where that is true?
It must be 2 x 3 x 7 +1, right? It's the number where I subtract 1 and the result can be divided evenly by each of these numbers
43
But that's not between 50 and 100, so I need a multiple of 42 +1 that is between 50 and 100.
How about 2 times (2x3x7) +1 or 85?