- WELCOME TO A LESSON ON SOLVING PERCENT PROBLEMS
USING THE PERCENT EQUATION.
THERE IS ANOTHER VIDEO
THAT SOLVES THE SAME TYPES OF PROBLEMS
USING THE PERCENT PROPORTION.
AND THE GOAL OF THIS VIDEO IS TO SOLVE PERCENT PROBLEMS.
SO THE IMPORTANT PART IN SETTING UP AND SOLVING AN EQUATION
IS GOING TO BE TO IDENTIFY THE KEY WORDS.
"OF" TRANSLATES TO MULTIPLICATION.
"IS" TRANSLATES TO EQUALS.
"WHAT" OR "WHAT NUMBER" TRANSLATES TO A VARIABLE.
IT COULD BE ANY VARIABLE BUT I USED N HERE.
AND IF WE'RE GIVEN THE PERCENT
WE NEED TO TRANSLATE THAT TO ITS DECIMAL FORM.
NOW, ONCE WE HAVE THE EQUATION WE WILL SOLVE THE UNKNOWN,
AND THEN MAKE SURE THAT THE ANSWER IS IN THE CORRECT FORM.
WHICH MEANS, IF THEY ASK FOR A NUMBER WE LEAVE IT AS A NUMBER.
IF THEY ASK FOR A PERCENT WE WRITE IT AS A PERCENT.
SO LET'S GO AHEAD AND GIVE IT A TRY.
I HAVE THE KEY WORDS OVER HERE IN THE UPPER RIGHT.
SO WHAT IS 12% OF 875?
SO THE FIRST WORD WE SEE IS "WHAT".
THAT TRANSLATES TO OUR VARIABLE.
LET'S CALL IT N.
"IS" MEANS EQUALS.
12%, WHICH MUST BE WRITTEN AS A DECIMAL 0.12,
"OF" MEANS MULTIPLY 875,
SO NOW WE SOLVE FOR THE UNKNOWN
WHICH IS VERY STRAIGHT FORWARD ON THIS PROBLEM.
WE JUST NEED TO FIND THIS PRODUCT.
0.12 x 875 = 105.
OKAY. NEXT QUESTION, 25 IS, SO WE WRITE DOWN 25 =.
THE NEXT KEY WORD WE SEE IS "WHAT,"
BUT IT DOES READ "WHAT PERCENT".
SO WE ARE GOING TO USE A VARIABLE.
I COULD USE N, BUT SINCE I KNOW I'M LOOKING FOR A PERCENT
I WILL USE P JUST TO REMIND ME
TO CONVERT MY ANSWER TO A PERCENT.
"OF" MEANS MULTIPLICATION 500.
SO IN ORDER TO SOLVE THIS EQUATION FOR P
WE NEED TO DIVIDE BY 500.
SO P = THIS FRACTION.
SINCE I KNOW I'M LOOKING FOR A PERCENT
I'M GOING TO GO AHEAD AND CONVERT THIS TO A DECIMAL.
25 DIVIDED BY 500 = 0.05.
NOW, REMEMBER I'M CONVERTING THIS TO A PERCENT
BECAUSE THAT'S WHAT IT ASKED FOR.
SO TO CONVERT A DECIMAL TO A PERCENT WE WILL MULTIPLY BY 100,
MOVE THE DECIMAL TO THE RIGHT TWICE,
AND ADD THE PERCENT SIGN.
NUMBER THREE, 2 IS, SO I WRITE DOWN 2 =.
4%, 0.04. "OF" MEANS MULTIPLY.
AND THEN "WHAT" OR "WHAT NUMBER" WILL CALL THIS N.
SO 2 IS 4% OF WHAT NUMBER?
AGAIN, IN ORDER TO SOLVE FOR N
WE HAVE TO DIVIDE BOTH SIDES BY 0.04.
SO WE WOULD HAVE N = 2 DIVIDED BY 0.04,
WHICH GIVES US 50.
LET'S SEE IF THAT MAKES SENSE.
2 IS 4% OF 50,
SO IT DOES MAKE SENSE THAT 2 IS A SMALL PERCENTAGE
OF THIS LARGER NUMBER 50.
AND GOING BACK UP TO NUMBER 2, 25 IS 5% OF 500.
AGAIN, IT MAKES SENSE THAT THIS NUMBER 25
IS A SMALL PERCENT OF THIS LARGER NUMBER 500.
AND THEN I'M BACK TO NUMBER ONE.
WHAT IS 12% OF 875?
IT SEEMS REASONABLE THAT 105 IS 12% OF THIS LARGE NUMBER.
LET'S GO AHEAD AND TAKE A LOOK AT A COUPLE APPLICATIONS NOW.
NOW WHEN WE SWITCH TO APPLICATIONS
WHAT WE'RE GOING TO DO IS BE ABLE TO READ THIS PROBLEM
AND THEN TRANSLATE IT INTO A SIMPLE QUESTION
LIKE ONE OF THE THREE PREVIOUS ONES.
THE BOOK STORE BUYS A TEXT BOOK FOR $80 AND SELLS IT $124.
WHAT IS THE PERCENT OF THE MARKUP?
WELL, FIRST WHAT IS THE MARKUP?
WELL, IF THEY PURCHASED THE BOOK FOR $80
AND THEY'RE SELLING IT $124
THE MARKUP WOULD BE HOW MUCH DO THEY ADD TO THIS 80
TO COME UP WITH $124?
WELL, WE COULD TAKE $124, SUBTRACT $80
AND THAT WOULD GIVE US OUR MARKUP,
AND THAT'S GOING TO BE $44.
SO, AGAIN, THE QUESTION IS, WHAT IS THE PERCENT OF MARKUP.
SO THE QUESTION WE NEED TO ANSWER IS
$44 IS WHAT PERCENT OF $80.
SO WE HAD TO DO A LITTLE PROBLEM SOLVING HERE.
AND THEN THE IDEA IS TO TRANSLATE THIS
INTO A SIMPLE PERCENT QUESTION,
AND THEN TRANSLATE THIS INTO AN EQUATION.
SO LET'S GO AHEAD AND DO THAT.
24 "IS" MEANS EQUALS, WHAT PERCENT,
SO I'LL USE P, "OF" MEANS MULTIPLICATION, AND $80,
SO 80.
SO NOW WE CAN SEE THAT WE DIVIDE BY 80 TO SOLVE FOR P.
AND, AGAIN, I USED P TO REMIND ME
THAT I'M LOOKING FOR A PERCENTAGE.
SO 44 DIVIDED BY 80 AND THEN CONVERT IT TO A PERCENTAGE.
SO TO CONVERT THIS TO A PERCENTAGE
REMEMBER WE MULTIPLY BY 100,
WHICH WILL GIVE US 55%,
WHICH IS OUR MARKUP.
LET'S GO AHEAD AND TAKE A LOOK AT ONE MORE.
TYPICALLY A SELF EMPLOYED PERSON MUST EARN 20% MORE
THAN A NON SELF EMPLOYED PERSON
TO HAVE THE SAME LEVEL OF COMPENSATION
DUE TO EXTRA TAXES AND EXPENSES.
SO IF A NON SELF EMPLOYED PERSON EARNS $18 PER HOUR
HOW MUCH WOULD A SELF EMPLOYED PERSON NEED TO EARN
TO HAVE AN EQUIVALENT INCOME.
OKAY. SO THERE'S KIND OF A LOT GOING ON HERE,
BUT THE IDEA IS SELF EMPLOYED PERSON MUST EARN 20% MORE.
SO THE QUESTION WE NEED TO ANSWER IS,
WHAT IS 120% OF $18 PER HOUR.
NOW, YOU MIGHT ASK WHY DID I SAY 120% WHEN IT ONLY STATES 20%.
WELL, IF THEY EARN 100%
OF WHAT THE NON SELF EMPLOYED PERSON EARNS
THEY'VE EARNED THE SAME AMOUNT $18 PER HOUR.
SO IT'S REALLY 100% + EXTRA 20% WHICH GIVES US THE 120%
THAT THE SELF EMPLOYED PERSON MUST EARN.
THIS REPRESENTS THE ORIGINAL $18 PER HOUR.
THIS REPRESENTS THE ADDITIONAL 20%.
OKAY. SO LET'S SEE IF WE CAN SET THIS UP AND SOLVE IT NOW.
"WHAT," WE'LL USE N, "IS" MEANS EQUALS,
120% AS A DECIMAL WOULD BE 1.2.
"OF" MEANS MULTIPLICATION.
AND $18 PER HOUR.
SO WE NEED TO FIND THIS PRODUCT 1.2 x 18, 21.6.
NOW, THIS REPRESENTS THE HOURLY RATE,
SO THAT WOULD BE $21.60 PER HOUR.
THANK YOU FOR WATCHING AND HAVE A NICE DAY.