SOLUTION: A bag contains 100 marbles, some red, the rest blue.if there are no more than one and a half times as many red marbles as blue ones in the bag at most how many red marbles are in t

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Question 1206722: A bag contains 100 marbles, some red, the rest blue.if there are no more than one and a half times as many red marbles as blue ones in the bag at most how many red marbles are in the bag? at least how many blue ones are in the bag?
Answer by ikleyn(52810) About Me  (Show Source):
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A bag contains 100 marbles, some red, the rest blue. If there are no more than one and a half times
as many red marbles as blue ones in the bag
(a) at most how many red marbles are in the bag?
(b) at least how many blue ones are in the bag?
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Let x be the number of blue marbles in the bag.
Then the number of red marbles is (100-x) (the rest).


We are given that

    100-x <= 1.5x.


From this inequality

    100 <= 1.5x + x

    100 <= 2.5x

    2.5x >= 100

       x >= 100/2.5 = 40.


ANSWER.  (b)  The number of blue marbles is at least 40.

         (a)  The number of red marbles is  100-x  <= 100-40 = 60.  (the number of red marbles is at most 60).

Solved.