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Problem Solving Strategies
Sometimes a problem will give you a final
result and the steps it took you to get there. In these types of
problems you would be asked to figure out what the starting point
must have been. This process is called
working
backwards.
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Let's start with
an easy example.
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After Bill gives 17 trading cards to his
friend Jim, he still has 68 cards of his own. How many trading
cards did Bill have before
he gave some away?
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Working
backwards,
you use the opposite, or
inverse
operation that Bill used when he gave the cards to Jim. Since
giving the cards away involves subtraction, you use
the opposite operation and add
17 to 68.
X - 17 = 68
X = 68 + 17 X = 85
Bill had 85 cards before he gave some to Jim.
Let's get a
little more complicated.
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Mary subtracted 8 from her age, and
divided that result by 3. The final answer was 4. How
old is Mary?
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Working backwards
we begin
by identifying which operations were used in the problem, and then
we will use the inverse operations
to get back to the
starting point...which is Mary's current age. In the problem,
Mary subtracted, and then divided. So to get to the starting
point we will work backwards, using the opposite operations.
That means we must first multiply (that will undo the division), and
then add (that will undo the subtraction).
(3) (4) = 12,
and then 12 + 8 = 2
Mary is 20 years old!!!
Now,
let's get serious!
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During the month of June,
Sheila deposited $385 into her checking account, wrote checks for
$98, and $617, and was charged $14 for new checks. If her
balance at the end of June was $899, what was her balance at the end
of May?
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During the month Sheila put
money into her account and took money out. You have to figure
how much money she had at the beginning of the month
To do that, start with the
ending balance and work backwards, using inverse
operations.
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Start with ending balance
Add
back $14 check charge
Add back $617 check
Add back $98 check
Subtract $385 deposit
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$899
+ 14
913
+617
1530
+ 98
1628
-385
$1249
balance at end of May
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