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The mean of a set of 4 numbers was 18. When a 5th number was added to the set, the mean dropped to 16. What was the number added to the set?

 

Can somebody walk me through?

 

Answer: 8

 

What I want to know: the steps to get 8

 

What I did: 

 

18 18 18 18

(18 - 16) + (18 - 16) + (18 - 16) + (18 - 16) = 8

8 +2 = 10

 

Where did I go wrong, and if you can't make sense of what I did, can you explain where I went wrong and how you would do it?

 

(and give me tips for the ISEE? thank you!)

 Nov 8, 2020
 #1
avatar+31320 
+1

Mean of the set of four numbers:

  (x1 + x2 + x3 + x4)/4 = 18   

Multiply both sides by 4, so

x1 + x2 + x3 + x4 = 4*18   ...(1)

 

Mean of the five numbers

(x1 + x2 + x3 + x4 + x5)/5 = 16

Multiply both sides by 5, so

x1 + x2 + x3 + x4 + x5 = 5*16   ...(2)

 

Replace x1 + x2 + x3 + x4 in (2) by using (1)

4*18 + x5 = 5*16

 

Subtract 4*18 from both sides

x5 = 5*16 - 4*18 

x5 = 80 - 72

x5 = 8

 Nov 8, 2020

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