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Put students into groups so no one is left out











































Word Problem - students divided into groups

   • They need to put students into groups so no one is left out.

           When they divide the class into two groups one student is left out.

           When they divide by three the same happens.

           They try 4,5,6 and still one student is left out.

   • if there are less than 100 students find the number of 5th graders

Comments for Put students into groups so no one is left out

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Oct 26, 2012
students divided into groups
by: Staff


Answer

Part I

n = number of 5th grade students



Summary of problem .

n < 100


2 groups = (n-1)/2 + 1


3 groups = (n-1)/3 + 1


4 groups = (n-1)/4 + 1


5 groups = (n-1)/5 + 1


6 groups = (n-1)/6 + 1


n-1 must be divisible by 1, 2, 3, 4, 5, and 6.

This means that n-1 must be the common multiple of 1, 2, 3, 4, 5, and 6.

There could be more than one answer to your question. At this point (in the solution process) we cannot tell.



Begin by computing the least common multiple (LCM)


LCM of 1,2,3,4,5,6


LCM of 1¹,2¹,3¹,2²,5¹,3¹*2¹


LCM = 1¹ * 3¹ * 2² * 5¹


LCM = 60


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Oct 26, 2012
students divided into groups
by: Staff


---------------------------------
Part II

(Other common multiples are 120, 180, and so on.)


The LCM, 60, is evenly divisible by 1, 2, 3, 4, 5, and 6.


If n-1 = 60, then n = 61


There are 61 students


This is the only answer because there are fewer than 100 students. The other common multiples of 1, 2, 3, 4, 5, and 6 are all greater than 100.



Final Answer:

61 students




Thanks for writing.

Staff
www.solving-math-problems.com



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