SOLUTION: The average (arithmetic mean) of the numbers 12, 28, 16, and x is between 22 and 24, inclusive. What is the least possible value of x?

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Question 771775: The average (arithmetic mean) of the numbers 12, 28, 16, and x is between 22 and 24, inclusive. What is the least possible value of x?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The average (arithmetic mean) of the numbers 12, 28, 16, and x is:
%2812%2B28%2B16%2Bx%29%2F4
given that the average is between 22 and 24, inclusive-means22%3C=x%3C=24; so, we have

22%3C=%2812%2B28%2B16%2Bx%29%2F4%3C=24......solve for x
22%3C=%2856%2Bx%29%2F4%3C=24....multiply by 4
22%2A4%3C=4%2A%2856%2Bx%29%2F4%3C=24%2A4
88%3C=56%2Bx%3C=96....subtract 56
88-56%3C=56-56%2Bx%3C=96-56
32%3C=x%3C=40
so, since 32%3C=x, the least possible value of x is 32

check:
%2812%2B28%2B16%2Bx%29%2F4.....plug in x=32
%2812%2B28%2B16%2B32%29%2F4=88%2F4=22 and 22%3C=22%3C=24