Math 20 - Lesson 54


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Transcript:
PORTLAND COMMUNITY COLLEGE MATHEMATICS TELECOURSE. A COURSE IN ARITHMETIC REVIEW PRODUCED AT
PORTLAND COMMUNITY COLLEGE.
AFTER THE LAST LESSON, I HOPE YOU BEGAN TO REALIZE WHAT MY FRIEND SAID BY THE STATEMENT
PERCENT IS A TALLY UNIT IN ALL OF BUSINESS. IN THIS LESSON WE WISH TO TRY TO TACKLE PROBLEMS
THAT BECOME MORE INVOLVED IN THEIR WORDING. IN THE LAST LESSON WE TACKLED SIMPLE STATEMENTS
OF THE FORM WHAT IS WHAT PERCENT OF WHAT. THAT'S GOING TO BE OUR SECRET NOW THAT HOPEFULLY
WE'RE GOOD AT THAT TYPE OF PROBLEM. IF A PROBLEM BECOMES MORE INVOLVED, WE'LL TRY TO RESTATE
IT LIKE THIS. LET'S LOOK AT THIS PROBLEM. A BUSINESS LOAN CHARGES SIMPLE INTEREST AT
A RATE OF 9.5 PERCENT PER YEAR. THE INTEREST FOR THE FIRST YEAR WAS $4,658. WHAT WAS THE
AMOUNT OF LOAN?
SEE, IN THIS PROBLEM WE HAVE THREE SENTENCES. OUR PROBLEM IS ONE OF SOMATICS NOT MATHEMATICS
AT FIRST. CAN WE RESTATE WHAT WE WANT IN TERMS OF WHAT WE HAVE IN ONE SIMPLE SENTENCE? REREAD
THIS AGAIN. NOW CAN YOU SEE THAT THIS IS SAYING THE SAME THING AS THIS SIMPLE STATEMENT: 9.5
PERCENT OF HOW MUCH IS 4658? NOW CLEARLY THERE'S NO PROBLEM THAT WE HAVE 9.5 PERCENT. THE INTEREST
FOR THE FIRST YEAR WAS THIS SO WE'RE TAKING 9.5 PERCENT OF SOMETHING. THAT'S WHAT I DON'T
KNOW. THEY TOLD ME THE INTEREST IS THIS. NOW THIS IS MORE A MATTER OF YOU KNOWING THEIR
LANGUAGE QUITE WELL OR YOUR BUSINESS QUITE WELL. BUT IN ANY CASE, BE ABLE TO TRANSLATE
IT TO A SIMPLE STATEMENT. THAT'S NOT EASY, BUT REALIZE THAT'S NOT MATHEMATICS EITHER.
THAT'S A MATTER BETWEEN YOU AND YOUR LANGUAGE.
BUT ONCE WE HAVE THE SIMPLE STATEMENT WE MAY CHOOSE METHOD ONE OR METHOD TWO. LET'S USE
METHOD ONE, THE TRANSLATION METHOD. 9.5 PERCENT IS .095.  THE OF IS TIMES. AND THE HOW MUCH
TRANSLATES TO? MY UNKNOWN, IN THIS CASE THE AMOUNT. AND THE IS TRANSLATES TO? EQUAL. AND
THE 458 IS ALREADY MATHEMATICS. AND WE HAVE A SIMPLE SENTENCE WHERE WE RECOGNIZE THAT
TO UNDO MULTIPLICATION WE DIVIDE BOTH SIDES BY THE MULTIPLIER OF THE UNKNOWN. SO NOW OUR
SENTENCE SAYS THAT A IS 4658 DIVIDED BY .095, WHICH IS $49,031.58. THE SECRET WAS TO TRY
TO GET THE SIMPLE STATEMENT OF OUR PROBLEM. LET'S TRY ANOTHER ONE. THE POPULATION OF A
TOWN THIS YEAR IS 14,100. LAST YEAR IT WAS 11,750. THIS YEAR'S POPULATION IS WHAT PERCENT
OF LAST YEAR'S? IN THIS PROBLEM MANY TIMES THEY DO THAT. THEY DO RESTATE YOUR PROBLEM
IN ONE SIMPLE SENTENCE, BUT THEY USE WORDS WHERE THEY COULD HAVE USED NUMBERS. WATCH
THIS NOW. THIS YEAR'S POPULATION IS SIMPLY 14,100. THEY TOLD ME SO, SO I SIMPLY REPLACE
THIS THREE WORD PHRASE WITH THE NUMBER THAT'S EQUAL TO IT. AND THE WORD IS, OF COURSE, IS
EQUAL. AND THE WORD WHAT IS MY UNKNOWN AND I'LL CALL IT P SINCE THEY'RE TELLING ME THEY
WANT PERCENT, BUT THE WORD PERCENT MEANS TIMES .01. THE WORD OF MEANS TIMES. AND LAST YEAR'S POPULATION,
THEY TOLD ME THAT. IT WAS 11,750. NOW THAT WE HAVE A SIMPLE SENTENCE, WE CAN SOLVE IT.
IN THIS CASE DOING THIS PORTION FIRST, WE GET 117.5 TIMES P. AGAIN WE RECOGNIZE THAT
THE UNKNOWN IS BEING MULTIPLIED AND TO UNDO MULTIPLICATION WE DIVIDE. SO THIS SAYS MY
PERCENT IS THIS DIVIDED BY THIS. DOING THAT WE GET 120. AND OF COURSE THAT'S PERCENT SO
THIS WORD SIMPLY CAN BE WRITTEN THAT WAY. THAT HAS NOTHING TO DO WITH MOVING THE DECIMAL
POINT. WE HAVE SIMPLY WRITTEN THIS WORD BY THIS SYMBOL. NOW REMEMBER 100 PERCENT MEANS
ALL OF. SO THIS IS MORE THAN A HUNDRED PERCENT SO IT MUST BE MORE THAN ALL OF. AND LAST YEAR
WE HAD 11 THOUSAND SO NOW WE MUST HAVE MORE THAN ALL OF THAT. AND 14 THOUSAND IS SOMEWHAT
MORE THAN 11 THOUSAND. SO AT LEAST WE'RE IN THE BALL PARK. BUT AGAIN THE SECRET WAS TO
SEE THIS SIMPLE STATEMENT OF THE PROBLEM AND RECOGNIZE THAT THE WORDS COULD HAVE BEEN REPLACED
BY NUMBERS.
LET'S TRY ANOTHER ONE. IF THERE IS A 4.2 PERCENT SALES TAX ON A $560 KITCHEN RANGE, HOW MUCH
IS THE TAX? NOW, CAN YOU RESTATE THAT PROBLEM AS A SIMPLER STATEMENT? HOW ABOUT THIS? ISN'T
THAT WHAT THEY REALLY WANT TO KNOW? WHAT IS 4.2 PERCENT OF $560? NOW TRANSLATE. WHAT IS
MY UNKNOWN. IS IS EQUAL. 4.2 PERCENT. IF I WANTED TO GET AWAY FROM A PERCENT, I MOVE
IT TWO PLACES AWAY, WHICH GIVES ME .042. OF IS TIMES 560. AND SEE IN THIS CASE IT'S TELLING
US EXACTLY WHAT TO DO. MY UNKNOWN IS THAT NUMBER TIMES THAT NUMBER, WHICH IS $23.52.
AGAIN THE SECRET LAY IN OUR BEING ABLE TO STATE IN A SIMPLE SENTENCE WHAT THE ORIGINAL
PERSON STATED IN MORE WORDS.
NOW IN THIS PROBLEM THEY DID ONCE AGAIN STATE THE SIMPLE SENTENCE FOR US IF WE CAN SEE IT.
THE BELLEVUE HIGH SCHOOL BASKETBALL TEAM WON 15 GAMES AND LOST 3. WHAT PERCENT OF ITS GAMES
DID IT WIN TO THE NEAREST WHOLE PERCENT? NOW CAN YOU FIND THE SIMPLE SENTENCE OF THE PROBLEM
THERE? THERE IT IS. NOW LET'S BEGIN TO TRANSLATE THAT WORD BY WORD. THE WHAT IS MY UNKNOWN.
PERCENT MEANS TIMES .01. OF MEANS TIMES. ITS GAMES, NOW DON'T LET THAT FOOL YOU. ITS
GAMES. ALL OF ITS GAMES IS NOT 15 AND 3. BUT IT WON 15 AND LOST 3, SO ITS GAMES WAS A TOTAL
OF 18 GAMES. NOW AGAIN DON'T LET THIS PHRASE FOOL YOU. DID IS A PAST TENSE OF THE WORD
IS. SO THAT'S EQUALS. AND WIN, WELL THAT'S THE 15 GAMES. SO WHAT PERCENT OF TOTAL GAMES
WAS THE WINS? ONCE YOU GET USED TO IT IT'S REALLY VERY SIMPLE. AND NOW IT'S SIMPLY A
MATTER OF SOLVING A SIMPLE EQUATION. DOING THE INDICATED MULTIPLICATION WE GET DIVIDING
BOTH SIDES BY THE MULTIPLIER OF THE UNKNOWN WE GET, AND CARRYING OUT THE INDICATED DIVISION
WE GET, 83.3333, BUT THE PROBLEM STATED TO THE NEAREST WHOLE PERCENT, AND HERE'S THE
WHOLE. THIS IS LESS THAN 5, SO I'LL ROUND IT DOWN. NOW WHEN YOU ARE USING ONE OF THESE
TWO METHODS, METHOD ONE OR METHOD TWO, WHEN THE PROBLEM IS ASKING FOR A PERCENT, WHEN
YOU'RE DONE, YOUR ABSOLUTELY DONE. IF YOU WISH TO SAY THIS AS PERCENT, THEN SIMPLY STICK
THE PERCENT SIGN ON. THIS IS SIMPLY OUR WAY OF SAYING THE WORD PERCENT, WHICH WAS IN OUR
SENTENCE. THAT'S ALL. BUT THE ANSWER IS 83 OF THOSE PERCENTS. NOW MANY STUDENTS BECOME
QUITE FRUSTRATED OVER THESE TYPES OF PROBLEMS. KNOW THAT MOST OF YOUR FRUSTRATION WILL LIE
WITH LANGUAGE, NOT MATHEMATICS. KNOWING THIS, DON'T ASK HOW DO I DO IT. BEFORE YOU HAVE
ASKED YOURSELF AND ANSWERED THE QUESTION: WHAT ARE THEY SAYING? THEN SAY THE SAME THING
MORE SIMPLY. LET ME ILLUSTRATE THIS. TYPICAL STATEMENT YOU MIGHT HEAR. A STORAGE DEPOT
RAISED ALL OF ITS RENTAL RATES 8 PERCENT OVER LAST YEAR'S. IF AN ANNUAL RENT WAS $240 THIS
YEAR, WHAT WAS THIS RENT LAST YEAR. NOW AS SEE, AS IT'S STATING, THAT'S QUITE A FEW WORDS.
NOW LET'S STATE IT DIFFERENTLY.
THIS YEAR'S RENT IS 100 PERCENT OF LAST YEAR'S RENT. CAN YOU SEE THAT'S SAYING THE SAME THING?
LAST YEAR'S RENT IS A HUNDRED PERCENT OF ITSELF, BUT WE RAISED IT ANOTHER 8 PERCENT, SO IT'S
A HUNDRED PLUS 8. NOW SEEING THAT WAS A LITTLE BIT TRICKY, BUT THAT'S LANGUAGE. BUT IN THIS
CASE, WHICH OF THESE DO WE KNOW? THIS YEAR'S RENT OR LAST YEAR'S RENT? SO IN REREADING
THE PROBLEM, IT'S THIS YEAR'S RENT THEY TOLD US. IT'S LAST YEAR'S RENT WE DON'T KNOW. SO
THIS YEAR'S RENT CAN BE REPLACED BY 240 BECAUSE THEY TOLD US. LAST YEAR'S, THAT'S MY UNKNOWN.
NOW TRANSLATING THIS 240 IS 108 PERCENT OF X. WE GET THIS. AND THIS IS EASY. SEE THIS
IS THE PURE MATHEMATICS, IN FACT, THE ONLY SPOT THAT WE HAVE PURE MATH. AND WE CAN JUST
LOOK AT THAT AND MAKE THE SIMPLE DECISION TO DIVIDE BOTH SIDES BY 1.08. DO THE ARITHMETIC
ON THE CALCULATOR, AND WE'RE DONE.
AND THE RENT LAST YEAR WAS INDEED LESS THAN THIS YEAR'S. THIS SPOT HERE IS THE PURE MATH.
THIS IS ARITHMETIC. THIS TRANSLATION REALLY IS STILL NOT HALF BAD. 240 IS 108 PERCENT
CHANGED INTO A DECIMAL OF LAST YEAR'S. SO THAT'S EASY. SO WHERE WAS THE PROBLEM? IN
GOING FROM MANY WORDS TO FEW WORDS. AND THAT'S FOUND BY ASKING WHAT ARE THEY SAYING? AND
SOMEHOW SAYING THE SAME THING MORE SIMPLY.
SO THIS IS WHERE YOU MUST FOCUS YOUR ATTENTION ON THESE PROBLEMS. IF YOU DO SO, IT BECOMES
FAIRLY EASY. ASKING HOW DO I DO IT WON'T HELP YOU UNTIL YOU HAVE FIRST ANSWERED THIS. LET'S
WORK ANOTHER PROBLEM PRETTY MUCH LIKE THAT ONE TO SEE IF WE CAN IDENTIFY SOME COMMONALITY,
SOMETHING ABOUT THE WORDING THAT WILL GIVE US A CLUE. LET'S SEE. A NEWSPAPER STATES THAT
THE TOWN'S CURRENT POPULATION IS 14,600, WHICH IS A 7 PERCENT INCREASE OVER LAST YEAR'S POPULATION.
WHAT WAS LAST YEAR'S POPULATION?
THERE'S A TENDENCY AT FIRST TO WANT TO TAKE 7 PERCENT OF THIS THEN SUBTRACT IT. BUT THEN
WE WOULD BE TAKING 7 PERCENT OF THE CURRENT ONE WHEN THIS CLEARLY SAYS THAT IT'S INCREASING
7 PERCENT OVER LAST YEAR'S. SO IF ANYTHING WE SHOULD TAKE 7 PERCENT OF LAST YEAR'S WHICH
WE DON'T EVEN KNOW. SO HOW CAN WE DO SOMETHING WE DON'T KNOW? SO SINCE OUR DIFFICULTY IS
HERE, IT'S BEST THAT WE STOP HERE AND REALIZE THAT NOWHERE DOES IT SAY THAT I WANT TO TAKE
7 PERCENT OF THIS. THIS SAYS IN FACT I WANT TO INCREASE IT BY 7 PERCENT. NOW, RECALL THIS
FROM OUR BEGINNING OF STUDYING OF PERCENTS: WHENEVER WE USE THE WORD "ALL OF" OR "THE
SAME AS" THEN YOU HAVE ONE HUNDRED PERCENT OF SOMETHING. THEREFORE, IF THE POPULATION
STAYED THE SAME AS, AGAIN THAT WORD SAME AS, IT WOULD BE 100 PERCENT OF WHAT IT WAS. LET'S
CALL IT L FOR LAST YEAR'S POPULATION. IF WE HAD SAID 8 PERCENT OF, SINCE THIS IS CERTAINLY
A GREAT, GREAT, GREAT DEAL LESS ISN'T IT? BUT THIS SAYS I WANT TO INCREASE. SO IT'S
GOING TO HAVE TO INCREASE ABOVE 100 PERCENT. IT'S GOING TO INCREASE 7 PERCENT ABOVE 100
PERCENT. SO WITH THAT KIND OF THINKING, SOMEWHERE ALONG THE LINE YOU HAVE TO SEE THIS, THAT
THIS YEAR'S POPULATION IS IN FACT 107 PERCENT OF LAST YEAR'S POPULATION OF LAST YEAR'S POPULATION.
LAST YEAR'S POPULATION, OF COURSE, IS 100 PERCENT OF ITSELF. AND YOU CAN SEE I TOOK
WHAT IT WAS IN ITSELF AND INCREASED IT 7 PERCENT TO GIVE ME THAT 107 PERCENT. ARE YOU BEGINNING
TO SEE THAT? IT'S LIKE SPEAKING ANY LANGUAGE. YOU MUST SPEAK IT AND TRY TO SEE IT TWO OR
THREE OR FOUR OR FIVE TIMES AND FINALLY IT BEGINS TO DAWN UPON YOU. BUT THEN AS SOON
AS YOU'VE BEEN ABLE TO STATE THIS, YOU HAVE THE SIMPLE IS PERCENT OF THE SENTENCE AND
YOU CAN BEGIN TO REPLACE WORDS BY NUMBERS. THIS YEAR'S POPULATION. DO WE KNOW THAT? IT
SAYS THAT THE CURRENT POPULATION, THIS YEAR'S, IS 14,600, SO THIS YEAR'S POPULATION IS 14,600
IS 107 PERCENT OF LAST YEAR'S POPULATION. BUT THAT'S WHAT I DON'T KNOW. SO, LET'S USE
A LETTER FOR THAT. SO NOW WE HAVE OUR SIMPLER IS PERCENT OF SENTENCE. AND WE CAN GO TO WHICH
EVER METHOD YOU PREFER. THE TRANSLATION OR THE IS OF. IF WE'RE USING THE IS OF RELATIONSHIP,
WE SEE THAT 14,600 IS ATTACHED TO THE IS, 107 IS ATTACHED TO THE PERCENT, AND L IS ATTACHED
TO THE OF, WHICH I DON'T KNOW. NOW EITHER BY CALCULATOR OR BY HAND WE SIMPLY SOLVE THIS
PROPORTION. SO 14,600 TIMES 100 DIVIDE BY 107, EQUALS, AND WE HAVE AND, OF COURSE POPULATIONS
DOESN'T ALLOW US TO HAVE FRACTIONAL PEOPLE, SO WE ROUND THIS OFF TO THE NEAREST WHOLE
PERSON WHICH IS 13,645. 13,645,
AND INDEED LAST YEAR'S POPULATION IS LESS THAN THIS YEAR'S AS WE SAY IT SHOULD BE. IF
WE WERE TO FIND THE INCREASE NOW JUST AS A CHECK, IF WE WERE TO SUBTRACT THESE TWO, WE
WOULD GET 5, 5, 9. SO WE ACTUALLY INCREASE THE POPULATION BY 955. SO WE COULD ASK THIS
QUESTION NOW. LET'S LOOK AT OUR INCREASE. OUR INCREASE 955 IS WHAT PERCENT OF WHAT IT
INCREASED FROM? AND IT'S INCREASING FROM THIS GOING TOWARDS THAT.
NOW WE'RE DOING THIS JUST TO CHECK THAT OUR THINKING IS REASONABLE ABOUT WHAT WE JUST
FINISHED. OKAY NOW TRANSLATING THIS TO OUR IS OF SITUATION AGAIN, THE 955 IS ATTACHED TO
THE IS. THE WHAT IS ATTACHED TO THE PERCENT. THE 13645 IS ATTACHED TO THE OF, AND OF COURSE
THIS STAYS AT 100.
NOW WORKING THIS PROBLEM WE GET 955 TIMES 100 DIVIDED BY 13645 AND WE GET IN FACT ROUND
IT OFF TO THE NEAREST WHOLE PERCENT THAT'S 7 PERCENT. SO OUR INCREASE, WHICH WAS ACTUALLY
955, WAS INDEED TO THE NEAREST WHOLE PERCENT. 7 PERCENT OF MY, OVER MY LAST YEAR'S POPULATION.
ACTUALLY IN BUSINESS MATH AND LATER IN ALGEBRA WE WILL ALLOW YOU YET A THIRD WAY OF SOLVING
THIS, WHICH WILL ALLOW YOU TO GO FROM THE WORDS TO ALGEBRA MORE QUICKLY. BUT IN ORDER
TO DO THIS, YOUR INSTRUCTOR WILL FIRST HAVE TO TEACH YOU SOME ALGEBRA ABOVE AND BEYOND
WHAT YOU'VE LEARNED IN THIS COURSE. SO IF YOU'RE USING ONLY THE KNOWLEDGE TAUGHT IN
THIS COURSE, THEN AT THIS STAGE OF SUCH PROBLEMS, YOU MUST RECOGNIZE THAT YOU'RE GOING TO HAVE
A READING PROBLEM. AND TRY TO APPROACH YOUR PROBLEM FROM THAT POINT OF VIEW. READING.
WHAT ARE THEY SAYING? CAN I SAY IT IN A SIMPLER MANNER? AND IF THEY'RE INCREASES SOMETHING,
YOU MUST REALIZE THAT WHAT ARE YOU INCREASING. IF YOU'RE INCREASING IT OVER WHAT IT WAS THEN
ANYTHING IS 100 PERCENT OF WHAT IT IS. IF YOU INCREASE IT ANOTHER 7 PERCENT, THEN IT'S
NOT GOING TO BE WHAT IT WAS. THAT'S A HUNDRED PERCENT INCREASED BY ANOTHER 7 PERCENT OR
107 PERCENT. DOES THAT HELP YOU JUST A LITTLE BIT TO GET A FEEL FOR THE REAL PROBLEM? AND
THAT IS: WHAT ARE THEY SAYING?
LET'S SPEND A FEW MOMENTS AND JUST PEEK AHEAD INTO ALGEBRA SO THAT PERHAPS YOU CAN SEE WHY
ONE WOULD EVEN WANT TO TAKE SUCH A COURSE. LET ME REDO THIS PROBLEM AS AN ALGEBRA STUDENT
MIGHT DO IT. AND DON'T WORRY ABOUT IF YOU CAN'T FOLLOW THE ALGEBRAIC MANIPULATION BECAUSE
OF COURSE YOU HAVEN'T HAD IT YET. BUT SEE IF YOU CAN SEE HOW EASY IT IS TO TRANSLATE
FROM THIS ENGLISH STATEMENT INTO AN ALGEBRA STATEMENT EVEN WITH THE LITTLE BACKGROUND
WE HAVE AT THIS POINT. NOW LET'S TAKE INTO ACCOUNT THE ENTIRE LONGER SENTENCE OR TWO
AND ASK OURSELVES WHAT ARE THEY REALLY SAYING IN TOTAL? AND SAY IN IT ALGEBRA. WHAT WE'RE
SAYING THAT LAST YEAR'S POPULATION INCREASED BY 7 PERCENT, AND SEE THAT'S 7 PERCENT AS
MATH, OF LAST YEAR'S POPULATION WILL GIVE THIS YEAR'S POPULATION, WHICH IS 14,600. NOW
BACK HERE, IF I HAVE LAST YEAR'S POPULATION, THAT'S THE SAME THING ISN'T IT AS ONE TIMES
LASTS YEAR. SO YOU'LL LEARN IN ALGEBRA THAT IF I HAVE SOMETHING LIKE THIS 5 OF LAST YEAR'S
INCREASED BY 2 OF LAST YEAR'S. WE CAN SEE THEN I HAVE NOT 7. I HAVE 7 OF LAST YEAR'S.
SO YOU'LL LEARN THAT IF ONE VARIABLE L HERE, PLUS.07 NOW, THEN GRAND TOTAL I HAVE 1.07
OF LAST YEAR'S. NOW THIS PROCESS OF GOING FROM HERE TO HERE IN ALGEBRA YOU WILL CALL
COMBINING LIKE TERMS, AND I DON'T EXPECT TO YOU NECESSARILY FOLLOW ME COMFORTABLY, BUT
AT LEAST YOU CAN GET THE FLAVOR OF IT. BUT AT THIS POINT YOU CAN SEE THAT TO UNDO MULTIPLYING
DIVIDE BOTH SIDES BY 1.07 AND DOING THAT DIVISION I GET EXACTLY WHAT WE HAD EARLIER. 13 THOUSAND
SOME ODD. BUT YOU SEE HOW EASY IT IS TO RESTATE THIS NOW USING A BROADER ASPECT OF ALGEBRA
THAN WE'VE ALLOWED OURSELVES YET? SIMPLY ONE OF LAST YEAR OR ALL OF LAST YEAR'S POPULATION
INCREASED BY 7 PERCENT OF LAST YEAR'S IS THIS YEAR'S, WHICH IS 14,600. SO WITH A LITTLE
BIT OF ALGEBRA, THIS TYPE PROBLEM WILL INDEED BECOME EASIER FOR YOU IN THE FUTURE. SO DO
LOOK FORWARD TO TAKING ALGEBRA SHORTLY AFTER THIS COURSE. IT WILL CERTAINLY PAY OFF.
BECAUSE THIS TYPE OF PROBLEM IS REALLY A MATTER OF EXPERIENCE, AND MUCH, MUCH EXPERIENCE AT
THAT, THIS PARTICULAR LESSON WE'LL START WITH FAIRLY SIMPLE PROBLEMS, SOMEWHAT MORE COMPLICATED
THAN THE LAST ONE BUT NOT MESSY PERHAPS AS YOU WOULD FIND IN A BUSINESS OR ACCOUNTING
COURSE. SO LET'S TRY THIS ONE.
THE COOPER'S HOUSE IS VALUED AT 72 THOUSAND DOLLARS AND RENTS FOR 600 DOLLARS PER MONTH.
WHAT PERCENT OF THE VALUE OF THE HOUSE IS THE ANNUAL RENT? VERY OFTEN IF YOU'RE READING
CAREFULLY WHEN YOU GET TO THE POINT WHERE THEY'RE ASKING YOU FOR SOMETHING, YOU FIND
THAT ALREADY IS A PERCENT OF AN IS. SO LET'S BEGIN TO READ THIS VERY CAREFULLY AND SEE
WHICH OF ITS WORDS WE CAN REPLACE BY NUMBERS FROM THE PREVIOUS SENTENCE OR SENTENCES. SO
IT SAYS WHAT PERCENT OF THE VALUE OF THE HOUSE? WELL THE VALUE OF THE HOUSE WE KNOW, SO THIS
ENTIRE PHRASE HERE, VALUE OF THE HOUSE, WE KNOW. THAT'S 72 THOUSAND DOLLARS. NOW WHAT
ELSE THERE IS THAT WE MIGHT KNOW? IS THE ANNUAL RENT. I DON'T KNOW THE ANNUAL RENT. I KNOW
THE MONTHLY RENT. BUT ANNUAL MEANS PER YEAR, SO IF I WERE TO TAKE 6 TIMES 12, I WOULD GET
7,200. SO NOW LET'S SEE WHAT WE HAVE. WHAT PERCENT OF IS TIMES THE VALUE OF THE HOUSE,
72 THOUSAND, IS, IS EQUAL THE ANNUAL RENT, WHICH IS 72 HUNDRED. AND NOW DOING THIS ARITHMETIC,
FOR THE SIMPLE REASON I CAN DO IT, I GET 720 TIMES P. AND THEN UNDOING THE MULTIPLICATION
BY DIVISION, I FINALLY GET THAT P IS 10 AND OF COURSE THAT'S PERCENT. SO THEY'RE PAYING
10 PERCENT OF THEIR ANNUAL PER YEAR. THEY'RE PAYING 10 PERCENT OF THE VALUE OF THE HOUSE
IN RENT.
WITHIN THIS HOMEWORK ASSIGNMENT DO LOOK FOR SIMPLE SENTENCES WITHIN THE TOTAL COMPLEX
OF THE PROBLEM WHERE IT IS AN OF IS PERCENT PROBLEM. THEN YOU SIMPLY IDENTIFY THE NOUNS
AND OBJECTS OF THE SENTENCE, TRY TO REPLACE THEM BY NUMBERS IF POSSIBLE, AND IF IT'S NOT
POSSIBLE, REPLACE IT BY A VARIABLE, THEN TRANSLATE IT, AND SOLVE IT. AGAIN WE NEED TO EMPHASIZE
THIS WILL TAKE A BIT OF PRACTICE AND WILL ENTAIL A FAIR AMOUNT OF FRUSTRATION, BUT BEAR
WITH IT. IT COMES WITH EXPERIENCE.
NOW SUMMARIZING WHAT WE'VE JUST BEEN DOING. WHEN YOU SEE A COMPLICATED OR A SERIES OF
SENTENCES EXPLAINING YOUR PROBLEM, THE FIRST THING YOU TRY TO DO, TRY TO LOCATE A SIMPLE
IS OF PERCENT SENTENCE AND REPLACE WORDS OR PHRASES BY NUMBERS FROM THE REST OF THE PROBLEM.
AND THEN, OF COURSE, TRANSLATE THEM INTO ALGEBRA WHERE IT WILL USUALLY BE A SIMPLE ALGEBRAIC
SENTENCE OR A PROPORTION. AND OF COURSE IF YOU CAN'T LOCATE THAT SIMPLE IS PERCENT OF
SENTENCE, THEN YOU MUST BE THE ONE TO RESTATE THE PROBLEM IN A SIMPLE IS PERCENT OF SENTENCE.
AND THERE IN IS GOING TO LIE YOUR PROBLEM. AND KNOW THAT THAT'S A MATTER OF YOUR OWN
PERSONAL USE OF LANGUAGE AND YOUR OWN ABILITY TO SEE WHAT IS BEING SAID IN A WRITTEN PAGE.
THIS IS YOUR MATH HOST, BOB FINNELL. GOOD LUCK.