Elementary POW, March 3-7,1997


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Salwa went to the mall to buy supplies for her math project. She spent half of what she had plus $2.00 in the first store; half of what she had left plus $1.00 in the second store; half of what she had left plus $1.00 in the third store; and in the last store, half of all she had. Three dollars were left over. How much money did she start with?

Remember to explain how you arrived at your answer.

This week's mentors are Miss Miller's Integrated Math II class from Cheshire High School in Cheshire, CT.
95 students answered this POW. It took us a while, but we enjoyed replying to each student. We hope all the email got through!

Students in Integrated Math II, grade 10 (Miss Miller)
Cheshire High School
Cheshire, CT

Correct Solutions submitted by:

Highlighted Solutions

Date:  Tue, 4 Mar 1997
From:  tracy and rich brondyke 
Subject:  math

The answer is $64.  I started at the end of the problem.  And went to the
starting of the problem.  The last store I know it is 6 because half of 6
is 3.  The third store I know it is 14 because half of what she spent +
1.00 is $8.00 and 14-8 is 6.  The second store I know it is $30.00 because
half of what she spent + 1.00 is $16.00.  30-16 is 14.  On the first store
she spent $64 because half of what she spent + 2.00 is $34 and 64-34=30.

Dustin Brondyke, age 8
.............................................................................


Date: Mon, 10 Mar 1997
From: Victor Osimitz 
Subject: Elementary POW

I worked backwards using a simple diagram. It started out like this (best
viewed in a monospace font):

IN    STORE #   OUT

       ---
      | 1 |
       ---

       ---
      | 2 |
       ---

       ---
      | 3 |
       ---

       ---
      | 4 |      $3.00
       ---

Salwa spent half of what she had at the last store, and if she left with
$3, she had $6 when she entered. 3 * 2 = 6


IN      #        OUT
       ---
$6    | 4 |      $3
       ---

Since she walked directly from #3 to #4, she had $6 left after #3, also.
She spent half of what she had  + $1 at the 3rd store, leaving her with
$14 before the 3rd store. 6 + 1 * 2 = 14

IN      #        OUT

       ---
$14   | 3 |      $3
       ---

       ---
$6    | 4 |      $3
       ---

She had the same amont of money as she left store 2, so Out-2 is also
$14. If she spent half of what she had + $1 at the second store, she
must have had $30 when she entered the 2nd store and $30 when she left
the 1st store. 14 + 1 * 2 = 30

IN      #        OUT

       ---
      | 1 |      $30
       ---

       ---
$30   | 2 |      $14
       ---

       ---
$14   | 3 |      $3
       ---

       ---
$6    | 4 |      $3
       ---

If she spent half of what she had + $2 at the first store, she started
with $64, as (30+2) * 2 = 64. So, the complete diagram is:

IN      #        OUT
       ---
$64   | 1 |      $30
       ---

       ---
$30   | 2 |      $14
       ---

       ---
$14   | 3 |      $3
       ---

       ---
$6    | 4 |      $3
       ---

Victor Osimitz
perseus1@worldnet.att.net
..............................................................................

Date: Fri, 7 Mar 1997
From: Beth ann Zampol 
Subject: answer to problem

This is how we did the problem:

-We started from the end and worked to the begining.

-First we took the 3.00 that was left over and multiplied it by 2.

3.00*2=6.00

-Then we added 1.00 to the 6.00 that we had.

1.00+6.00=7.00

-We then did 7.00*2.00=14.00

-Then we did 14.00+1.00=15.00

-We then did 15.00*2.00=30.00

-Then we did 30.00+2.00=32.00

-The last thing we did was 32.00*2.00=64.00

- 64.00 dollars was our answer.


Woodward Academy Busey School
Bette Ann, Brittany, Alex
...............................................................................

We went to the web page Tim describes below and found an *ANIMATED* answer!
Cheshire High School students

Date:  Thu, 6 March 1997
From:  SFSS74C@prodigy.com
Subject:  Elem. POW Submission 3/7

My answer is a web page at http://pages.prodigy.com/SFSS74C/epow0307.htm

Tim Peterson
Grade 6
Homeschooled
SFSS74C@prodigy.com
Rochester, NY

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