6th Grade Math Textbook, Fundamentals

(Marvins-Underground-K-12) #1
 &KDSWHU

Problem-Solving Strategy:


Work Backward


Objective To solve problems using the strategy Work Backward

Problem 1: Before going to work, Dad took half the money that Mom left
in an envelope on the kitchen table. Later, Susan took half of what was in the
envelope when she left for school. Still later, Wally took half of what was left
when he went to school. When Mom retrieved the envelope upon returning
home from work that afternoon, she found exactly $12 in it. How much money
was originally in this envelope?


11-12


Problem-Solving Strategies
1.Guess and Test
2.Organize Data
3.Find a Pattern
4.Make a Drawing
5.Solve a Simpler Problem
6.Reason Logically
7.Adopt a Different Point of View
8.Account for All Possibilities


  1. Work Backward
    10.Consider Extreme Cases


Read to understand what is being asked.
List the facts and restate the question.
Facts: Three members of the family successively
took half the money in an envelope.
After this, $12 remained.
Question:How much did the envelope initially hold?

Select a strategy.
By using the strategy Work Backward, you can start
from the amount that remains at the end of the day
and figure out how much was in the envelope at the
beginning of the day.

Apply the strategy.


  • Because Wally left $12 in the envelope, he must
    have taken $12. So there was $24 in the envelope
    before he got to it.

  • When Susan saw the envelope, it must have held exactly $48 (twice $24).
    She would have grabbed half of the money, or $24, and left half, $24,
    in the envelope.

  • It follows that Dad would have seen twice this $48, or $96,
    in the envelope. He took $48 and left $48 in the envelope.
    So Mom must have originally left $96 in the envelope.


Check to make sure your answer makes sense.
You can check your solution by running through the scenario
from start to finish.


  • Mom left $96 in an envelope.

  • Dad takes half of $96, or $48, and leaves $48 in the envelope.

  • Susan takes half of $48, or $24, and leaves $24 in the envelope.

  • Wally takes half of $24, or $12, and leaves $12 in the envelope.

  • Mom returns home and finds $12 in the envelope.
    The answer checks.

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