SOLUTION: Robert is now 78 years old and his friend Charlie 70.How many years ago was Charlie only 3/4 as old as Robert?

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Question 10093: Robert is now 78 years old and his friend Charlie 70.How many years ago was Charlie only 3/4 as old as Robert?
Answer by longjonsilver(2297) About Me  (Show Source):
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well, we can take off a set number of years, and this will be off both ages: call it x. Eventually (age of Charlie)/(age of Robert) will be 3/4, so

now we have 70/78, last year we would have had 69/77 etc etc... in general we have (70-x)/(78-x) and this needs to be 3/4, so

(70-x)/(78-x) = 3/4
4(70-x) = 3(78-x)
280-4x = 234-3x
280-x = 234
-x = -46
--> x = 46

So, 46 years ago!

CHECK! 46 years ago, ages of 2 would have been 24 and 32, whose fraction is 24/32 which is 12/16 which is 3/4.

jon.