SOLUTION: Jane and jeffert had some marbles. Jane had 40 % more marble than jeffery. When jane lost 12 marbles and gave 16 marbles to jeffery, both of them had an equal number of marbles. Ho

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Question 1201329: Jane and jeffert had some marbles. Jane had 40 % more marble than jeffery. When jane lost 12 marbles and gave 16 marbles to jeffery, both of them had an equal number of marbles. How many marbles did each of them have at first
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52777)   (Show Source): You can put this solution on YOUR website!
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Jane and jeffert had some marbles. Jane had 40 % more marble than jeffery.
When jane lost 12 marbles and gave 16 marbles to jeffery, both of them had an equal number
of marbles. How many marbles did each of them have at first
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Jeffery - x marbles originally.

Jane 1.4x marbles originally.


After the described changes, we have this equation

    1.4x - 12 - 16 = x + 16.


Simplify and find x

    1.4x - 28 = x + 16

    1.4x - x = 16 + 28

        0.4x =   44

           x =   44/0.4 = 440/4 = 110.


ANSWER.  Originally, Jeffery had 110 marbles;  Jane had 1.4*110 = 154 marbles.

Solved.

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Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


Another tutor has provided a typical formal algebraic solution starting with the fact that Jane had 40% more marbles than Jeffery at the beginning.

Let's try a different approach, starting with the fact that the two of them ended up with the same number of marbles. It might or might not turn out to make it easier to solve the problem this way.

x = number each ended up with

Before Jane gave 16 marbles to Jeffery, Jane had x+16 marbles and Jeffery had x-16 marbles.

And before Jane lost 12 marbles, she had x+28 marbles.

Jane originally had 40% more marbles then Jeffery, so she had 140/100 = 7/5 as many as Jeffery:







They each ended up with x= 126 marbles, so originally Jane had x+28 = 154 marbles and Jeffery had 126-16 = 110 marbles.

ANSWER: Jeffery started with 110 marbles; Jane started with 154.

It looks to me as if this approach to solving the problem is MORE work than the method shown by the other tutor....

However, you should always be open to the idea of trying different ways to set up a problem for solving. Sometimes a way that seems less obvious turns out to make solving the problem much easier.
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