Question 1210591
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Three brothers—Leo, Sam, and Jax—are sharing a supply of energy bars during a hike. Leo starts the trip with a backpack 
full of bars. He eats 3 1/2 bars. After eating them, the ratio of the bars he has left to the bars he started with is 
exactly 3:4. Sam then takes the remaining bars. He eats half of them plus half a bar more. Jax takes what is left. He eats 
half of that amount plus half a bar more. After Jax is finished, there are exactly 2 bars left in the backpack. How many 
energy bars did Leo start with?
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<pre>
Let X be the number of energy bars Leo did start with (the unknown value under the problem's question).

Leo eats 3.5 bars first.

The number of bars left is x-3.5.


Write the proportion as stated in the problem

    {{{(x-3.5)/x}}} = {{{3/4}}}.


From this proportion

    4x - 14 = 3x,

    4x - 3x = 14,

       x    = 14.


So, the answer to the problem's question is 14 energy bars.


You may check that this answer satisfies the problem's conditions,
Thus, all the problem's conditions are consistent and do not contradict each other.
</pre>

At this point, the problem is solved completely.