SOLUTION: If the average (arithmetic mean) of 31, 41, and p is between 29 and 47, inclusive, what is the least possible value of (p-7)squared?

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Question 1023154: If the average (arithmetic mean) of 31, 41, and p is between 29 and 47, inclusive, what is the least possible value of (p-7)squared?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
29+%3C=+%2831%2B41%2Bp%29%2F3+%3C=+47
<==> 87+%3C=+p%2B72+%3C=+141
<==> 15+%3C=+p+%3C=+69
<==> 8+%3C=+p-7+%3C=+62
==> 64+%3C=+%28p-7%29%5E2+%3C=+3844
The least possible value of %28p-7%29%5E2 is now clear.