Question 583447: A group of students decided to create gift bags of cookies to give to the elderly. Students brought in as many cookies as they wanted to donate, and they gathered their cookies together before creating little gift bags. They gathered a lot of cookies, and they noticed some interesting patterns. When the cookies were divided into groups of two, there was one cookie left over. When the cookies were divided into groups of three, there was one cookie left over. When the cookies were divided into groups of four, there was one cookie left over. When the cookies were divided into groups of five or six, there was one cookie lefty over. But when the cookies were into groups of seven, there were no cookies left over. Based on these clues, what is the smallest number of cookies that the students could have gathered?
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! When the cookies were divided into groups of two, there was one cookie left over. When the cookies were divided into groups of three, there was one cookie left over. When the cookies were divided into groups of four, there was one cookie left over. When the cookies were divided into groups of five or six, there was one cookie lefty over. But when the cookies were into groups of seven, there were no cookies left over.
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Enter these equations in your scientific calculator:
Y1 = (x-1)/2
Y2 = (x-1)/3
Y3 = (x-1)/4
Y4 = (x-1)/5
Y5 = (x-1)/6
Y6 = x/7
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Solution: x = 301
======================
Found by looking for an x-value that has whole number
y-values for ALL of the 6 equations. (Use the TABLE of a TI-84.
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Cheers,
Stan H.
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Answer by Edwin McCravy(20054)  (Show Source):
You can put this solution on YOUR website!
Here's another way.
The number 2×2×3×5 = 60 is divisible by 2,3,4,5, and 6.
So 1 less than the number we're looking for has all these factors,
and so is a multiple of 60.
So we are looking for a number that is one more than a multiple of
60 that is also a multiple of 7.
Write down the first few multiples of 60:
60, 120, 180, 240, 300, 360, 420
Add 1 to each
61, 121, 181, 241, 301, 361, 421
Divide each by 7. You'll get a decimal each time until you come to
301. When you divide 301÷7 and you get 43
So the answer is 301.
Edwin
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