How would you approach this math problem?

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1

<p>How would you a approach a math problem like this (this is a grid in from Barrons):</p>

<p>Five people shared a prize of $100. Each one received a whole number of dollars, and no two people recieved the same amount. If the largest share was $30 and the smalled share was $15, what is the most money that the person with the third largest share could have received?</p>

<p>BTW, the answer is 19.</p>

2

<p>Okay, so we can do this: </p>

<p>1: 30
2: 20
3: 19
4: 16
5: 15</p>

<p>We know the money left, $55, is to be divided among the prizewinners. In order to maximize the 3rd largest, we now can assume the fourth largest is 16 (to maximize the values of 2nd and 3rd). Giving us 55-16 = 39. Now it's easy to see that the maximization of the 3rd largest would mean the smallest non-zero difference between 2nd and 3rd, so we can split 39 into 19 and 20. Thus, 19 is the answer.</p>