Question 619179: The sum of all the 29 people i.e physicians, surgeons and nurses is 696. If the age of each physician, surgeon and nurse be 1 year, 6 year, and 3 years more, then the average age of whole off staffwould have been 3 years more. If the number of surgeon is a square root of a two digit no. which is also a perfect cube, then the no of nurses in hospital is
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The sum of all the ages of 29 people i.e physicians, surgeons and nurses is 696.
If the age of each physician, surgeon and nurse be 1 year, 6 year, and 3 years more, then the average age of whole off staff would have been 3 years more.
If the number of surgeon is a square root of a two digit no. which is also a perfect cube, then the no of nurses in hospital is
:
Let n = number of nurses
Let p = number of physicians
Let s = number of surgeons
;
We should be able to find the number of surgeons from the statement:
"If the number of surgeon is a square root of a two digit no. which is also a perfect cube"
The two digit number would be 64, so we have 8 Surgeons
Therefore nurses and physicians: 29 - 8 = 21
:
s = 8
n + p = 21
:
If the age of each physician, surgeon and nurse be 1 year, 6 year, and 3 years more, then the average age of whole off staff would have been 3 years more.
 = 3
Replace s with 8, mult equation by 29
p + 6(8) + 3n = 3(29)
p + 48 + 3n = 87
p + 3n = 87 - 49
p + 3n = 39
:
We know p + n = 21, use elimination here
p + 3n = 39
p + n = 21
-------------subtraction eliminates p, find n
2n = 18
n = 9 nurses
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