SOLUTION: Mary is 24 years old.Mary is twice as old as Ann when Mary was as old as Ann now.How old is Ann now?

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Question 120241: Mary is 24 years old.Mary is twice as old as Ann when Mary was as old as Ann now.How old is Ann now?
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
Mary is 24 years old. Mary is twice as old as Ann was when Mary was as old as Ann now. How old is Ann now?

The best way to learn to work word problems is 
to "practice by cheating".  Practice by looking 
up the answer in the back of the book and then 
check that answer in the words to see why it is 
the correct answer.  That's an excellent way to 
learn to work word problems. 

That's because to set up a word problem when you 
DON'T know the answer requires the exact same 
reasoning it takes to check the word problem when
you DO know the answer.  You just "check" it the 
same way using an unknown instead of a known 
number.  

So first I'll tell you the answer.  Then we'll 
check it, and then use the same words to set up 
the equation.

The answer is 18.  Let's check that in the words
to see just why 18 is correct:

Mary is 24 years old.  Ann is 18 years old.  Therefore 
the difference in their ages is 24-18 or 6 years.  
Mary, 24, is twice as old as Ann was when Mary was
as old as Ann now. Since the difference in their ages 
is 6 years, when Mary was 18, Ann was 18-6 or 12, and 
24, which is Mary's age now, equals twice Ann's age
6 years ago, which was 12.  

Now let's let Ann's age be A instead of 18, and use 
the same words:

Mary is 24 years old.  Ann is A years old.  Therefore 
the difference in their ages is 24-A years. 
Mary, 24, is twice as old as Ann was when Mary was 
as old as Ann now. Since the difference in their ages 
is 24-A years, when Mary was A, Ann was A-(24-A), and 
24, which is Mary's age now, equals twice Ann's age 
24-A years ago, which was A-(24-A).  
 
So we take those last words

>>...24, which is Mary's age now, equals twice Ann's 
age 24-A years ago, which was A-(24-A)...<<

which shortens to

>>...24...equals twice A-(24-A)...<<

and becomes the equation

24 = 2[A-(24-A)]

which you can easily solve and get A = 18.

So to practice setting up word problems,

1. "Cheat" first by looking up the answer.
2. Check that answer to see why it is correct 
   by observing what turns out to be equal.
3. Use the exact same reasoning using an 
   unknown.  Then when you get the part where
   something was equal, which told you the
   answer was correct when you checked it
   with the answer, just set those two
   quantities equal, and solve for the 
   unknown. 

Edwin






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