# 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?

Algebra ->  Algebra  -> Customizable Word Problem Solvers  -> Age -> 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?      Log On

 Ad: Over 600 Algebra Word Problems at edhelper.com Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

 Word Problems: Age Solvers Lessons Answers archive Quiz In Depth

 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(8909)   (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```