SOLUTION: The mean of five numbers is 56. Four of the numbers are the same. The average of one of the five numbers and the fifth number is 80. What are the five numbers?

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Question 690922: The mean of five numbers is 56. Four of the numbers are the same. The average of one of the five numbers and the fifth number is 80. What are the five numbers?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The mean of five numbers is 56. Four of the numbers are the same.
The average of one of the five numbers and the fifth number is 80.
What are the five numbers?
:
Let a = the 4 numbers that are the same
Let b = the fifth number
%284a%2Bb%29%2F5 = 56
4a + b = 5(56)
4a + b = 280
:
" The average of one of the five numbers and the fifth number is 80."
%28a%2Bb%29%2F2 = 80
a + b = 2(80)
a + b = 160
:
Subtract the above equation from the 1st equation
4a + b = 280
a + b = 160
---------------subtracting eliminates b, find a
3a = 120
a = 120/3
a = 40
:
Find b
40 + b = 160
b = 160 - 40
b = 120
:
What are the five numbers?
40,40,40,40,120