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 1206721: 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?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52810)   (Show Source): You can put this solution on YOUR website!
.
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?
~~~~~~~~~~~~~~~~~~~~~~~~ 

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.



Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


Note that, while the statement of the problem implies we need to solve an inequality, we can in fact find the solution by solving the corresponding equation and then using common sense to answer the questions.

In the limiting case, the ratio of red to blue marbles is 1.5:1, or 3:2.

100 marbles in the ratio 3:2 means 60 red marbles and 40 blue. (You can probably do that part of the problem mentally; if not, there are simple formal algebraic ways.)

Using that result for the limiting case, we can use logical reasoning and the wording of the problem to see that there at most 60 red marbles, which means at least 40 blue ones.

ANSWERS: At most 60 red; at least 40 blue
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