SOLUTION: the average of 4 distinct integers is 152. if the largest number out of these 4 integers is 201. what is the least possible value of the smallest positive integer amongst the 4

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Question 935430: the average of 4 distinct integers is 152. if the largest number out of these 4 integers is 201. what is the least possible value of the smallest positive integer amongst the 4
Answer by MathLover1(20850) About Me  (Show Source):
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Let the 4 different positive integers be A, B, C, and D such that A+%3C+B+%3C+C+%3C+D
The average (arithmetic mean) of four distinct positive integers is 152, and the largest number highlight%28D=201%29.
So, %28A%2BB%2BC%2BD%29%2F4+=+152
This means A%2BB%2BC%2BD+=+608
since D=201
A%2BB%2BC%2B201+=+608
A%2BB%2BC+=+608-201
A%2BB%2BC+=+407....since the sum of A%2BB%2BC+ is 407, and
since A is the smallest positive integer, the highlight%28least%29 highlight%28possible%29 value of the A is highlight%28A=7%29
then,
B%2BC+=+407-A
B%2BC+=+400 => since both highlight%28less%29 than highlight%28D=201%29, then highlight%28B=C%29 and both are highlight%28200%29