Question 130: Ralph is four times as old as Frank. In 20 years, Ralph will be twice as old as Frank. How old are ralph and Frank?
Answer by terrtwo(10)   (Show Source):
You can put this solution on YOUR website! If we use R for Ralph and F for Frank, the initial relationship between their ages is R = 4F
Ralph's age in twenty years will be R + 20, or his age now plus 20 years.
Frank's age will likewise be F + 20 in twenty years
Therefore the second equation we can write is
--> (R + 20) = 2(F + 20)
If we then substitute 4F for R in the second equation
--> (4F + 20) = 2(F + 20)
We then distribute the 2:
--> 4F + 20 = 2F + 40
Subtract 20 from both sides;
--> 4F + 20 - 20 = 2F + 40 - 20
--> 4F = 2F + 20
Subtract 2F from both sides
--> 4F - 2F = 2F + 20 - 2F
--> 2F = 20
Divide both sides by 2;
--> 2F/2 = 20/2
--> F = 10
When we substitute 10 for F back into the original equation (R = 4F);
--> R = 4*10 = 40
Hence Frank is now 10 and Ralph is 40
Twenty years from now, Frank will be 30 and Ralph will be 60, or twice Frank's age
So the answer is F = 10 and R = 40
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