SOLUTION: Tom's graduating class has 288 students. At the graduation ceremony, the students will sit in rows with the same number of students in each row. If there must be at least 10 rows a

Algebra ->  Divisibility and Prime Numbers -> SOLUTION: Tom's graduating class has 288 students. At the graduation ceremony, the students will sit in rows with the same number of students in each row. If there must be at least 10 rows a      Log On


   

Question 1210667: Tom's graduating class has 288 students. At the graduation ceremony, the students will sit in rows with the same number of students in each row. If there must be at least 10 rows and at least 15 students in each row, then there can be x students in each row. What is the sum of all possible values of x?
Answer by ikleyn(53979) About Me  (Show Source):
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Tom's graduating class has 288 students. At the graduation ceremony, the students will sit in rows
with the same number of students in each row. If there must be at least 10 rows and at least 15 students in each row,
then there can be x students in each row. What is the sum of all possible values of x?
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Let r be the number of rows.


Then we have this equation, expressing the total number of students

    x*r = 288.       (1)


Consider it as a decomposition of number 288 into the product of integer positive numbers x and r.

They want you find the sum of all possible factors x of 288 in equation (1), such that

    x >= 15,  r >= 10.


Let's make the Table of such divisors x and r


    x    r    
---------------              

    16   18

    18   16

    24   12


We want the sum of values x in first column.  It is 16 + 18 + 24 = 58.


ANSWER.  The number under the problem's question is 58.

Solved.