SDRAWKCAB KROW (WORK BACKWARDS)

WE USE THE STRATEGY OF WORKING BACKWARDS WHEN WE HAVE THE ANSWER TO A PROBLEM OR THE POINT AT WHICH WE ENDED. IN THIS CASE, WE CAN TRACE OUR WAY BACK TO SEE WHAT WAS HAPPENING AT THE BEGINNING.

FOR EXAMPLE, LET’S SAY THAT BALRAJ HAS $143 IN HIS CASH REGISTER RIGHT NOW. HIS CASH REGISTER TAPE SHOWS HE RANG UP A $42 ORDER, ISSUED A CREDIT OF $28, AND RANG UP AN OTHER ORDER OF $77. HOW MUCH WAS IN HIS CASH REGISTER WHEN HE BEGAN?

TO SOLVE THIS PROBLEM, WE START WITH THE ENDING NUMBER OF 143 AND THEN SUBTRACT THE ORDERS AND ADD THE CREDIT. WE NEED TO DO THE OPPOSITE SINCE WE ARE WORKING BACKWARDS (WE HAVE TO UNDO WHAT WE DID). SO, WE HAVE 143 – 42 + 28 – 77. THIS GIVES US THE ORIGINAL AMOUNT OF $52.

WORK BACKWARDS TO FIND THE SOLUTION TO EACH PROBLEM.

1) 2) 3) 4) IF I TAKE MY MYSTERY NUMBER, MULTIPLY IT BY 2, ADD 4, DIVIDE BY 5, AND SUBTRACT 2, I GET 0. WHAT IS MY MYSTERY NUMBER?

FIREFIGHTER STAN IS HARD AT WORK PUTTING OUT AN OFFICE FIRE. HE STARTED ON A CERTAIN RUNG OF A LADDER, WENT UP 3 RUNGS, DOWN 5 RUNGS, UP 1 RUNG, DOWN 2 RUNGS, DOWN 7 RUNGS, AND UP 4 RUNGS. HE IS NOW ON THE 12 TH RUNG. WHAT RUNG DID HE START ON?

SASHA SPENT ONE-THIRD OF HER MONEY ON SHOES, THEN ANOTHER $36 ON A HAIRCUT AND STYLE. AFTER THAT, SHE SPENT HALF OF WHAT WAS LEFT ON A DRESS AND FINALLY SPENT $12 ON LUNCH. SHE HOW HAS $30. HOW MUCH MONEY DID SHE BEGIN WITH?

TED AND NED ARE PLAYING A DICE GAME THAT THEY CREATED. THE RULE FOR SCORING IN THIS GAME IS AS FOLLOWS: EACH PERSON BEGINS WITH THE SAME NUMBER OF POINTS. AT THE END OF EACH ROUND, THE PERSON WITH THE LOWEST SCORE ON HIS DICE WINS. AT THE END OF EACH ROUND, EACH PERSON DEDUCTS THE TOTAL NUMBER OF POINTS ON HIS DICE, BUT THE LOSER ALSO HAS TO DEDUCT THE WINNER’S POINTS AS WELL. THE FIRST FIVE ROUNDS GO AS FOLLOWS: ROUND 1: TED = 5, NED = 8; ROUND 2: TED = 9, NED = 4; ROUND 3: TED = 7, NED = 6; ROUND 4: TED = 3, NED = 10; ROUND 5: TED = 9, NED = 5. IF TED’S FINAL SCORE IS 168, HOW MANY POINTS DID EACH MAN BEGIN WITH?

1) IF I TAKE MY MYSTERY NUMBER, MULTIPLY IT BY 2, ADD 4, DIVIDE BY 5, AND SUBTRACT 2, I GET 0. WHAT IS MY MYSTERY NUMBER?

SINCE WE ARE WORKING BACKWARDS, WE WILL DO THE OPPOSITE OF EACH STEP. 0 + 2 = 2 2 X 5 = 10 10 – 4 = 6 6 ÷ 2 = 3. OUR MYSTERY NUMBER IS 3.

2) FIREFIGHTER STAN IS HARD AT WORK PUTTING OUT AN OFFICE FIRE. HE STARTED ON A CERTAIN RUNG OF A LADDER, WENT UP 3 RUNGS, DOWN 5 RUNGS, UP 1 RUNG, DOWN 2 RUNGS, DOWN 7 RUNGS, AND UP 4 RUNGS. HE IS NOW ON THE 12 TH RUNG. WHAT RUNG DID HE START ON?

WORKING BACKWARDS MEANS BEGINNING ON THE 12 TH RUNG AND UNDOING THE STEPS.

12 – 4 = 8 8 + 7 = 15 15 + 2 = 17 17 – 1 = 16 16 = 5 = 21 21 – 3 = 18.

HE BEGAN ON THE 18 TH RUNG.

3) SASHA SPENT ONE-THIRD OF HER MONEY ON SHOES, THEN ANOTHER $36 ON A HAIRCUT AND STYLE. AFTER THAT, SHE SPENT HALF OF WHAT WAS LEFT ON A DRESS AND FINALLY SPENT $12 ON LUNCH. SHE HOW HAS $30. HOW MUCH MONEY DID SHE BEGIN WITH?

LET’S BEGIN AT THE END WITH $30.

30 + 12 = 42 42 X 2 = 84 84 + 36 = 120 120 IS 2/3 OF WHAT SHE STARTED WITH.

120 = (2/3)X. NOW DIVIDE BOTH SIDES BY 2/3.

120 ÷ 2/3 = 120 X 3/2 = 120/1 X 3/2 = 360/2 = 180.

SO, SASHA BEGAN WITH $180.

4) TED AND NED ARE PLAYING A DICE GAME THAT THEY CREATED. THE RULE FOR SCORING IN THIS GAME IS AS FOLLOWS: EACH PERSON BEGINS WITH THE SAME NUMBER OF POINTS. AT THE END OF EACH ROUND, THE PERSON WITH THE LOWEST SCORE ON HIS DICE WINS. AT THE END OF EACH ROUND, EACH PERSON DEDUCTS THE TOTAL NUMBER OF POINTS ON HIS DICE, BUT THE LOSER ALSO HAS TO DEDUCT THE WINNER’S POINTS AS WELL. THE FIRST FIVE ROUNDS GO AS FOLLOWS: ROUND 1: TED = 5, NED = 8; ROUND 2: TED = 9, NED = 4; ROUND 3: TED = 7, NED = 6; ROUND 4: TED = 3, NED = 10; ROUND 5: TED = 9, NED = 5. IF TED’S FINAL SCORE IS 168, HOW MANY POINTS DID EACH MAN BEGIN WITH? LE’T BEGIN AT THE END AGAIN! TED HAS A FINAL SCORE OF 168 POINTS.

HE LOST ROUND 5, SO WE NEED TO ADD BOTH SCORES (5+9). 168 + 14 = 182.

HE WON ROUND 4, SO WE ONLY NEED TO ADD HIS SCORE OF 3. 182 + 3 = 185.

HE LOST ROUND 3, SO WE ADD BOTH SCORES (7+6). 185 + 13 = 198.

HE LOST ROUND 2, SO WE ADD BOTH SCORES (9+4). 198 + 13 = 211.

HE WON ROUND 1, SO WE ONLY ADD HIS SCORE OF 5. 211 + 5 = 216.

BOTH MEN STARTED WITH 216 POINTS.

MORE WORKING BACKWARDS PROBLEMS AND RESOURCES ONLINE

• HTTP://WWW.STUDYZONE.ORG/TESTPREP/MATH4/D/WORKBACKS4L.CFM

• HTTP://WWW.STUDYZONE.ORG/MTESTPREP/MATH8/G/WORKBACKL.CFM

• HTTP://WWW.MATHSTORIES.COM/STRATEGIES_WORKING_BACKWARD.HTM

• HTTP://WWW.MATHOLYMPIAD.INFO/PAGES/WORKINGBACKWARDS.ASPX

• HTTPS://WWW.YOUTUBE.COM/WATCH?V=AUVSIYDMYDS • HTTPS://WWW.YOUTUBE.COM/WATCH?V=5FFWTSMEEJW • HTTPS://WWW.TEACHERVISION.COM/PRINTABLE/SKILL-BUILDER/54651.HTML