Fred picked four numbers out of a hat. The average of the four numbers is 9. If three of the numbers are 5, 9 and 12, then what is the fourth number?

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Let the four numbers be:

5, 9, 12, and x

Given the average of the four number is  9.

We know that the average:

Av. = (sum of all numbers)/ total number of numbers

==> 9 = (5+9+12+x)/4

==>  9 = (26+ x)/4

Multiply by 4:

==> 36 = 26 + x

==> x= 36- 26= 10

==> the fourth number = 10

skiazo's profile pic

skiazo | Student, Grade 11 | (Level 1) eNoter

Posted on

another method which you might find easier is to first find the total of all four numbers and because we have the mean then it is easier to find.

total of all numbers= 9x4=36

then you add up the numbers we do know: 5+9+12=26

so now you subtract the total of the 4 numbers from the total of the three numbers: 36-26= 10

have fun :)

william1941's profile pic

william1941 | College Teacher | (Level 3) Valedictorian

Posted on

If the average of 4 numbers is X, then the sum of the differences between each of the numbers and X has to be equal to zero.

Here we have the average as 9. Let the fourth number to be found be D.

So we have the differences as (5-9) , (9 - 9), (12 - 9) and (D-9)

Now , (5-9) + ( 9 -9) + (12 - 9) + (D-9) = 0

=> -4 + 0 + 3 + D - 9 =0

=> D - 10 = 0

=> D = 10.

Therefore the fourth number is 10.

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