- A SALESPERSON RECEIVES A 6.9% COMMISSION ON HER SALES.
IF HER TOTAL SALES FOR THE MONTH ARE $4,100,
WHAT IS HER COMMISSION?
SO TO DETERMINE OUR COMMISSION,
WE NEED TO ANSWER THE QUESTION, WHAT IS 6.9% OF $4,100?
TO FIND THE PERCENT OF A NUMBER,
WE CONVERT THE PERCENT TO A DECIMAL AND MULTIPLY.
SO THE QUICKEST WAY TO ANSWER THIS QUESTION
WOULD BE TO FIND THE PRODUCT OF 0.069,
WHICH IS THE PERCENT EXPRESSED AS A DECIMAL,
AND 4,100.
LET'S GO AHEAD AND DO THIS ON THE CALCULATOR.
WE HAVE 0.069 x 4,100, WHICH IS EQUAL TO 282.9.
AND WHILE WE'RE HERE, ONE METHOD
FOR CONVERTING A PERCENT OR DECIMAL
IS TO REMOVE THE PERCENT SIGN AND DIVIDE BY 100.
NOTICE 6.9 DIVIDED BY 100 DOES GIVE US 0.069.
THE OTHER METHOD IS TO REMOVE THE PERCENT SIGN
AND MOVE THE DECIMAL POINT TO THE LEFT TWO PLACES.
BUT, AGAIN, OUR PRODUCT IS 282.9,
WHICH MEANS HER COMMISSION WOULD BE $282.90.
BUT LET'S ALSO SET THIS UP MORE FORMALLY
USING A PERCENT EQUATION AS WELL AS A PERCENT PROPORTION.
TO SET UP THE PERCENT EQUATION, YOU WOULD USE THESE KEYWORDS.
SO NOTICE HOW IN OUR BASIC QUESTION HERE
THE FIRST WORD WE SEE IS "WHAT," WHICH REPRESENTS THE UNKNOWN.
SO WE USE A VARIABLE WHEN WE SEE THE WORD "WHAT"
OR "WHAT NUMBER."
LET'S USE C FOR COMMISSION.
NEXT WE HAVE "IS".
"IS" MEANS EQUALS SO NOW WE HAVE C EQUALS.
NEXT WE HAVE OUR PERCENTAGE,
WHICH, AGAIN, MUST BE EXPRESSED AS A DECIMAL,
WHICH WOULD BE 0.069.
NEXT WE HAVE THE WORD "OF".
"OF" MEANS MULTIPLY.
SO WE HAVE TIMES AND THEN WE HAVE OUR NUMBER 4,100.
NOTICE HOW THIS PRODUCT IS THE SAME PRODUCT THAT WE HAD ABOVE,
SO WE KNOW THIS IS EQUAL TO 282.9.
NOW, LET'S ALSO SET THIS UP USING THE PERCENT PROPORTION.
THE PERCENT PROPORTION ALWAYS FITS THIS FORM HERE.
WELL, NOTICE FOR THE SECOND RATIO
WE HAVE A DENOMINATOR OF 100.
AND BECAUSE WE'RE GIVEN THE PERCENT IS 6.9%
AND A PERCENT IS ALWAYS A NUMBER COMPARED TO 100,
THE 6.9 GOES OVER THE 100.
AND THEN BECAUSE WE KNOW THE COMMISSION
IS PART OF THE SALES AMOUNT,
THE UNKNOWN OF THE VARIABLE GOES IN THE NUMERATOR
AND THE WHOLE IS THE ENTIRE SALES AMOUNT OF 4,100.
WE CAN ALSO USE KEYWORDS TO SET UP THIS PROPORTION
WHERE THE FIRST RATIO WOULD BE "IS" OVER "OF."
SO LOOKING AT OUR QUESTION AGAIN,
BECAUSE IT SAYS "WHAT IS,"
THE NUMERATOR IS THE UNKNOWN OR THE VARIABLE C.
AND THEN BECAUSE IT SAYS "OF $4,100,"
$4,100 IS IN THE DENOMINATOR OF OUR SECOND RATIO.
NOW THAT WE HAVE A PROPORTION,
WE CROSS-MULTIPLY AND SOLVE FOR C.
SO WE'D HAVE C x 100 = 4,100 x 6.9.
WELL, C x 100 = 100C = 4,100 x 6.9.
NOTICE HERE TO SOLVE FOR C,
WE WOULD DIVIDE BOTH SIDES BY 100.
NOTICE HERE ON THE LEFT, THIS SIMPLIFIES TO 1C OR C.
AND NOW TO EVALUATE THIS ON THE CALCULATOR,
WHICH WE KNOW SHOULD GIVE US 282.9.
SO OUR NUMERATOR IN PARENTHESIS
IS 4,100 x 6.9, CLOSE PARENTHESIS,
DIVIDED BY 100.
AND AS EXPECTED, WE GET THE SAME RESULT.
OKAY.
I HOPE YOU FOUND THIS HELPFUL.