Once again, make sure
that you fully understand the problem and
what it is asking you to do. In this problem,
someone is left with $12 after spending
1/3 of his money and losing 2/3 of the
what was left. First of all, I think this
guy should be a little more careful!
As you get ready to solve this one, look
over the possible problem solving strategies
and see which one(s) may help you the most.
One strategy is to work backwards. You
are given the final amount of money the
man had with events leading up to what
he has left. Let's try working backwards
starting with the money he has left and
working backwards to the amount he started
with.
As you begin to work backwards, you can
even try to look at the facts you are
given backwards starting with the money he had
left. You know he had $12 at the end of
the day. He lost 2/3 of the amount before
he had $12. Therefore, you need to find
a number that when multiplied by 2/3 equals
$12. Algebraically, it can be set up as:
2/3 * Y = $12
(3/2)2/3 * Y = 12 * 3/2
Y = 36/2
Y = $18
If you are not able to use algebra to
solve for the missing number, you may want
to use guess and check to find the missing
number that when multiplied by 2/3 equals
12.
We continue to work backwards and we know
that the man had $18 before he lost his
money and ended up with $12.
Now we need to basically do the same
thing with the final step in finding
his original
amount of money. You know that after he
spent money he ended up with $18. You know
that $18 is 1/3 of the money he started
with, so all you need to do is to multiply
$18 by 3 or add $18 three times.
$18 x 3 = $54
By working backwards, you found out that
the man started with $54.
In your answer, be sure to include
the strategy you used to solve the problem,
in this case working backwards. Be clear
and specific as to the steps you took to
arrive at the answer of $54. A problem
like this may be a multiple choice problem
with you having to explain how you solved
it, a short answer problem, or even an
extended response question. As long as
you know how to solve the problem and explain
your solution clearly you will receive
all the assigned points. |
