Question 281389: three tired and hungry men went to sleep with a bag of apples. one man woke up, ate 1/3 of the applaes, then went back to sleep. later a second man woke up and ate 1/3 of the remaining alpples. when he was fiished there were 8 apples left. how many apples were in the bag originally
* create a solution that uses algebre and show all steps uses
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! x = number of apples in the bag originally
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We are told the first man ate 1/3 of the apples.
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That means that 2/3 of the apples were left in the bag.
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We are told the second man ate 1/3 of the apples that he found in the bag.
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BUT notice that he did NOT eat 1/3 of x apples.
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He ate 1/3 of the 2/3 of the apples that were left in the bag.
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1/3*2/3 = 2/9
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So the second man ate 2/9 of the x total apples.
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That means the two men ate a total of 1/3x plus 2/9x, leaving 8 apples in the bag.
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1/3x + 2/9x = 3/9x + 2/9x = 5/9x
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However, notice that the above tells us how many apples they ate, not how many apples are left.
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x - 5/9x is how many apples are left, which is 9/9x - 5/9x = 4/9x.
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4/9x is how many apples are left.
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4/9x = 8
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4x = 72
x = 18
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Checking our work...
How many apples are 1/3 of 18?
1/3*18 = 6
So the first man ate 6 apples, leaving 12 in the bag.
How many apples are 1/3 of 12?
1/3*12 = 4
So the second man ate 4 apples, leaving 8 apples in the bag.
Correct.
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Answer:
There were 18 apples in the bag originally.
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Done.
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