SOLUTION: The average age of consisting doctors and lawyers is 40 . If the doctors average age is 35 and the lawyers average age is 50 , find the ratio of the number of doctors to the number

Question 1106037: The average age of consisting doctors and lawyers is 40 . If the doctors average age is 35 and the lawyers average age is 50 , find the ratio of the number of doctors to the number of lawyers

Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = the number of doctors
Let = the number of lawyers
Let = the total of the ages of the doctors
Let = the total of the ages of the lawyers
---------------------------------------------
(1)
(1)
and
(2)
(2)
= the total of ages of doctors and lawyers
-------------------------------------------------
(3)
(3)
(3)
(3)
(3)
(3)
(3)
The ratio is 2 to 1

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

This is essentially a mixture problem; you are mixing doctors and lawyers and getting an average age of the whole group.

Here is an easy way to solve mixture problems....

(1) The overall average age of 40 is "twice as close" to the average age of the doctors (35) as it is to the average age of the lawyers (50):
That is, 50-40=10; 40-35=5. 5 is half of 10; so 40 is twice as close to 35 as it is to 50.
(2) That "twice as close" means the number of doctors has to be twice the number of lawyers.

So the ratio of the number of doctors to the number of lawyers is 2:1.
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