Question 1201329
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Another tutor has provided a typical formal algebraic solution starting with the fact that Jane had 40% more marbles than Jeffery at the beginning.<br>
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.<br>
x = number each ended up with<br>
Before Jane gave 16 marbles to Jeffery, Jane had x+16 marbles and Jeffery had x-16 marbles.<br>
And before Jane lost 12 marbles, she had x+28 marbles.<br>
Jane originally had 40% more marbles then Jeffery, so she had 140/100 = 7/5 as many as Jeffery:<br>
{{{(x+28)/(x-16)=7/5}}}
{{{7(x-16)=5(x+28)}}}
{{{7x-112=5x+140}}}
{{{2x=252}}}
{{{x=126}}}<br>
They each ended up with x= 126 marbles, so originally Jane had x+28 = 154 marbles and Jeffery had 126-16 = 110 marbles.<br>
ANSWER: Jeffery started with 110 marbles; Jane started with 154.<br>
It looks to me as if this approach to solving the problem is MORE work than the method shown by the other tutor....<br>
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.<br>