John's Losing His MarblesDate: 8/26/96 at 11:29:16 From: Raymond Subject: Losing Marbles Dear Dr. Math, Kindly advise the following : John has twice as many green marbles as red marbles. When John lost 42 green marbles, he had half as many green marbles as red marbles. How many marbles had he altogether at first? I look forward to hearing from you soon. Thanks and best regards. Date: 8/26/96 at 15:20:59 From: Doctor Robert Subject: Re: Losing Marbles Let x be the number of red marbles that John originally had. Then, according to the problem, the original number of green marbles is 2x. Now when John lost 42 green marbles, he must have had 2x-42 green marbles. According to the problem, this number is one half of the number of red marbles. We can write the equation 2x-42 = (1/2)x 4x - 84 = x 3x = 84 x = 28. So, he orginally had 28 red marbles and 56 green marbles for a total of 94 marbles. Unfortunately, John is losing his marbles. You can check to see whether the answer is correct. If John loses 42 green marbles he then has only 14 green marbles which is (1/2) of 28, the number of red marbles. So, we know we're right. That's what I like about word problems! -Doctor Robert, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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