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- WELCOME TO AN EXAMPLE THAT WILL SHOW
HOW TO FIND THE REQUIRED FINAL EXAM SCORE IN ORDER
TO RECEIVE AN A IN A COURSE WHERE THE COURSE GRADE
IS BASED UPON WEIGHTED AVERAGES.
LET'S ASSUME YOUR COURSE IS BASED
UPON THE FOLLOWING CATEGORIES
WITH THE GIVEN WEIGHTS LISTED HERE ON THE LEFT.
HOMEWORK IS WORTH 20% OF THE GRADE,
THE PROJECT IS WORTH 10% OF THE GRADE,
THE TEST WORTH 40% OF THE GRADE,
AND THE FINAL EXAM IS WORTH 30% OF THE GRADE.
WHAT FINAL EXAM PERCENTAGE DO YOU NEED TO RECEIVE
AN "A" GRADE IN THE COURSE?
SO YOUR HOMEWORK AVERAGE IS 93%, WHICH IS WORTH 20% OF THE GRADE.
YOUR PROJECT GRADE IS 88% WORTH 10% OF YOUR GRADE.
YOUR TEST AVERAGE IS 86% WORTH 40% OF YOUR GRADE.
AND THE UNKNOWN, WHICH WE'LL CALL X
WILL BE THE FINAL EXAM GRADE.
SO X WILL BE THE LOWEST POSSIBLE FINAL EXAM SCORE
TO RECEIVE AN "A" GRADE.
SO WHAT WE'LL DO IS SET UP THE GRADE
USING THIS WEIGHTED AVERAGE FORMULA,
AND THEN SOLVE FOR X, THE UNKNOWN.
BEFORE WE DO THIS, NOTICE THE LOWEST "A" IS 89.5%.
SO OUR EQUATION WILL BE 89.5
IS EQUAL TO THE HOMEWORK PERCENTAGE, WHICH IS 93%,
WHICH WE'LL JUST WRITE AS 93 x THE WEIGHT OF 20%
AS A DECIMAL WOULD BE 0.2.
PLUS THE PROJECT GRADE OF 88% TIMES THE WEIGHT OF 10%
AS A DECIMAL 0.1.
PLUS THE TEST AVERAGE OF 86% x THE WEIGHT OF 40% OR 0.4
AS A DECIMAL.
AND THEN FINALLY, THE LAST GRADE IS A FINAL EXAM PERCENTAGE,
WHICH WE DON'T KNOW, THAT'S x X THE WEIGHT OF 30% OR 0.3.
SO NOW IF WE SOLVE THIS EQUATION FOR X,
WE CAN DETERMINE THE LOWEST POSSIBLE FINAL EXAM SCORE
TO RECEIVE AN A GRADE IN THE COURSE.
LET'S GO AHEAD AND TAKE THIS EQUATION OVER TO THE NEXT SLIDE
AND SOLVE FOR X.
LET'S BEGIN TO SIMPLIFY THE RIGHT SIDE OF THIS EQUATION.
SO WE'LL FIND THIS PRODUCT, THIS PRODUCT,
THIS PRODUCT, AND THIS PRODUCT.
SO WE'LL HAVE 89.5 = 93 x 0.2 = 18.6 + 88 x 0.1 = 8.8 + 86
x 0.4 = 34.4 + X x 0.3 = 0.3X.
NOW WE'LL COMBINE THE LIKE TERMS ON THE RIGHT SIDE
OR ADD THESE DECIMALS.
SO WE'LL HAVE 89.5 = THIS SUM'S = 61.8, AND WE HAVE + 0.3X.
NOW WE'RE DOWN TO A BASIC TWO STEP EQUATION,
SO WE'LL SUBTRACT 61.8 ON BOTH SIDES.
THIS DIFFERENCE IS 27.7.
SO FOR THE LAST STEP TO SOLVE FOR X,
WE'LL DIVIDE BOTH SIDES BY 0.3.
SO X, THE MINIMUM FINAL EXAM SCORE TO RECEIVE AN "A,"
WILL BE EQUAL TO THIS QUOTIENT HERE.
SO WE'LL GO TO THE CALCULATOR.
WE HAVE 27.7 DIVIDED BY 0.3.
SO THE EXACT VALUE WOULD BE 92.3 REPEATING,
WHICH WE CAN WRITE AS 92.3 WITH A BAR ACROSS THE 3.
BUT LET'S GO AHEAD AND ASSUME THERE WON'T BE ANY DECIMALS
IN THE FINAL EXAM PERCENTAGE,
WHICH MEANS IN ORDER TO SCORE AN "A",
WE WOULD HAVE TO ROUND UP TO THE NEXT PERCENTAGE OR 93%.
AND AS FOR ROUND DOWN,
THIS WOULD NOT GIVE US A REQUIRED 89.5% FOR THE "A".
SO WE'LL CONCLUDE, YOU MUST SCORE 93% OR HIGHER
ON THE FINAL TO RECEIVE AN "A" IN THE COURSE.
I HOPE YOU FOUND THIS EXPLANATION HELPFUL.
AND I ALSO HOPE YOU GET AN "A" IN THE COURSE.