Answer: 16
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Work Shown
x = the missing number
The arithmetic mean of 3 values is the result of adding them up, then dividing the sum over 3.
(17+24+x)/3 = 19
(41+x)/3 = 19
41+x = 3*19
41+x = 57
x = 57-41
x = 16
The missing number is 16.
The average of the set {16,17,24} is 19.
Check: (16+17+24)/3 = 57/3 = 19
The answer is confirmed.
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Here's another approach
Imagine there are 3 towers of blocks.
Tower A is 17 blocks tall, tower B is 24 blocks tall, and tower C is of unknown height.
Now imagine rearranging the blocks so the towers end up being of equal height. That equal height is the average.
Tower A originally had 17 blocks. It needs 2 more blocks to get to 19
Tower B was 24 blocks tall. It needs to lose 5 blocks to get to 19.
The net change is -5+2 = -3, which then leads to 19+(-3) = 16 which is the mystery number we solved for in the previous section. Tower C is 16 blocks tall. It is 3 blocks short of the average height.