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