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Lawyers vs. Doctors

The average age of a group of lawyers is 50. The average age of a group of doctors is 35. The average age of both doctors and lawyers taken as a group is 40. What is the ratio of the number of lawyers to the number of doctors?

Can you solve this?

Did you "think" it through...or calculate the ratio using algebraic manipulations?


Source: MacMillan Math : Grade 7, 1987, p. 291

Hint: Put your pen/pencil down....Try to reason it out given the three "average" values...


Solution Commentary: Suppose every lawyer was 50 and every doctor was 35. Then, for the group's average age to be 40, which group dominates the average age...and by what factor....this should lead to a good "ratio" (and rational) thought....

Now, can you prove it algebraically?