SOLUTION: The arithmetic mean or average of the age of a group of doctors and lawyers is 40. If the average age of the doctors is 35 and the average age of the lawyers is 50, then what is th

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Question 242660: The arithmetic mean or average of the age of a group of doctors and lawyers is 40. If the average age of the doctors is 35 and the average age of the lawyers is 50, then what is the ratio of the number of doctors to the number of lawyers?
Found 2 solutions by Theo, stanbon:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the ratio of doctors to lawyers is 2/1 calculated as follows:

d = number of doctors
l = number of lawyers.

total age for doctors is d*35

total age for lawyers is l*50

total age for both is (d+l) * 40

since the total age for both is equal to the total age for doctors plus the total age for lawyers, we have:

35*d + 50*l = 40*(l+d)

this becomes:

35*d + 50*l = 40*l + 40*d

subtract 40*l from both sides of the equation and subtract 35*d from both sides of the equation and you get:

10*l = 5*d

divide 5 from both sides of the equation and you get:

d = 2*l

this means that the number of doctors is 2 times the number of lawyers.

take any value of doctors.

say 52

number of lawyers must be equal to 26 since d = 2*l.

total age for doctors is 52*35 = 1820

total age for lawyers is 26*50 = 1300

total age for doctors and lawyers is 3120

divide 3120 by total number of doctors and lawyers of 52+26 = 78 and you get:

average age of doctors is 40.

your answer is that the ratio of doctors to lawyers is 2 to 1.







Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The arithmetic mean or average of the age of a group of doctors and lawyers is 40. If the average age of the doctors is 35 and the average age of the lawyers is 50, then what is the ratio of the number of doctors to the number of lawyers?
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Let # of doctors be "D" ; let # of lawyers be "L"
Sum of ages of doctors and lawyers = (D+L)*40 years
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Sum of ages of doctors and lawyers = 35D + 50L
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Equation:
Sum = Sum
40D + 40L = 35D + 50L
5D = 10L
D/L = 2:1
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Cheers,
Stan H.