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If the average of three numbers is 19 two of the numbers are 17 and 24, what is the third number

1 Answer

2 votes

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.

User Muhib Pirani
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