Ex - Find the points needed to receive an a in a class based on total points

- IN THIS PROBLEM WE WILL ADDRESS SEVERAL COMMON GRADE QUESTIONS FOR A COURSE WHERE THE GRADE IS BASED UPON TOTAL POINTS. WITH FOUR WEEKS LEFT IN CLASS, YOU HAVE EARNED 575 POINTS OUT OF 650. THE CLASS IS BASED UPON 1,000 POINTS. WHAT IS YOUR CURRENT GRADE IN THE COURSE, HOW MANY MORE POINTS MUST YOU EARN TO RECEIVE AN "A" GRADE, AND FINALLY, WHAT PERCENT MUST YOU EARN FROM THE REMAINING POINTS TO RECEIVE AN "A" IN THE CLASS? SO BECAUSE A PERCENT IS A NUMBER COMPARED TO 100, TO FIND THE CURRENT GRADE IN THE COURSE WE'RE GOING TO FORM A FRACTION USING THE EARNED POINTS AND TOTAL POINTS, AND THEN MULTIPLY IT BY 100 TO CONVERT TO PERCENTAGE. SO WE'RE REALLY FINDING THE FRACTION EARNED OF 100 TO FIND THE PERCENT. SO THE CURRENT GRADE IS GOING TO BE EQUAL TO THE POINTS EARNED, WHICH IS 575 DIVIDED BY THE AVAILABLE TOTAL POINTS RIGHT NOW, WHICH WOULD BE 650. THIS WOULD GIVE THE GRADE AS A DECIMAL. AND THEN TO CONVERT TO A PERCENTAGE, WE WILL MULTIPLY IT BY 100. SO WE'RE FINDING THIS FRACTION OF 100 TO FIND OUR GRADE AS A PERCENTAGE. SO NOW WE'LL GO TO THE CALCULATOR. WE HAVE 575 DIVIDED BY 650. THIS IS THE GRADE AS A DECIMAL. NOW WE'LL MULTIPLY IT BY 100. NOTICE HOW THIS IS EQUIVALENT TO MOVING THE DECIMAL POINT TO THE RIGHT TWO PLACES. SO THE CURRENT GRADE IS APPROXIMATELY 88.46 OR 88.46%. SO, AGAIN, NOW WE'LL ADD THE PERCENT SYMBOL. SO WE HAVE 88.46%. LOOKING AT OUR SCALE, THIS WOULD BE IN THE B RANGE. SO OUR GOAL HERE IS TO GET THIS GRADE UP TO AN "A". NOTICE THE LOWEST "A" IS 89.5%. SO LET'S ANSWER QUESTION B ON THE NEXT SLIDE. WE WANT TO KNOW HOW MANY MORE POINTS MUST YOU EARN TO RECEIVE AN "A" GRADE. AGAIN, NOTICE THE LOWEST "A" GRADE WOULD BE 89.5%. BUT FOR THIS QUESTION, I THINK IT WILL BE A LITTLE BIT EASIER IF WE LOOK AT THE GRADE AS A DECIMAL. SO LET'S GO AHEAD AND CONVERT THIS TO A DECIMAL. WE WOULD DIVIDE BY 100 OR MOVE THE DECIMAL POINT TO THE LEFT TWO PLACES THAT WOULD BE 0.895. SO YOU MUST HAVE AT LEAST THIS GRADE IN ORDER TO RECEIVE AN "A" FOR THIS SEMESTER. WE ALSO HAVE AN UNKNOWN, THAT WOULD BE THE NUMBER OF POINTS THAT WE MUST EARN TO RECEIVE THE "A". SO LET'S LET X EQUAL THE MINIMUM NUMBER OF POINTS THAT MUST BE EARNED TO RECEIVE AN "A". SO, AGAIN, WE CAN FIND THE GRADE AS A DECIMAL BY TAKING THE EARNED POINTS AND DIVIDING BY THE TOTAL POINTS. BUT NOW THE EARNED POINTS CONSIST OF THE UNKNOWN X AND THE POINTS ALREADY EARNED. SO WE CAN SET UP AN EQUATION WHERE X WOULD BE THE POINTS THAT WE MUST EARN TO RECEIVE AN "A", PLUS THE POINTS EARNED DIVIDED BY THE TOTAL POINTS IN THE COURSE, WHICH WOULD BE 1,000. WE WANT THIS TO BE EQUAL TO 0.895. AND NOW IF WE SOLVE THIS EQUATION FOR X, WE'LL KNOW THE MINIMUM NUMBER OF POINTS THAT WE MUST EARN TO RECEIVE AN "A". SO LETS FIRST CLEAR THIS FRACTION BY MULTIPLYING BOTH SIDES OF THE EQUATION BY 1,000.   SO ON THE LEFT SIDE THIS SIMPLIFIES TO 1, SO WE JUST HAVE X + 575. ON THE RIGHT SIDE MULTIPLYING BY 1,000, WE CAN JUST MOVE THE DECIMAL POINT TO THE RIGHT THREE PLACES. THAT WOULD BE 895. AND NOW TO SOLVE FOR X, WE'LL SUBTRACT 575 ON BOTH SIDES, SO WE HAVE X = 320. WHICH MEANS YOU MUST EARN AT LEAST 320 POINTS TO RECEIVE AN "A". THIS IS ON TOP OF THE 575 POINTS THAT YOU'VE ALREADY EARNED. OF COURSE YOU COULD EARN MORE THAN 320 POINTS, BUT THIS IS A MINIMUM NUMBER OF POINTS THAT YOU MUST EARN TO RECEIVE AN "A" IN THE CLASS. IF YOU EARN EXACTLY 320 POINTS, YOU WOULD RECEIVE THE LOWEST "A" GRADE POSSIBLE. NOW LET'S GO AHEAD AND ANSWER THE LAST QUESTION, WHAT PERCENT MUST YOU EARN ON THE REMAINING POINTS IN THE CLASS TO RECEIVE THIS "A" GRADE? WELL, FROM PART B, WE KNOW YOU HAVE TO EARN 320 POINTS. AND THEN FOR THE POSSIBLE POINTS, THERE'S A TOTAL OF 1,000 POINTS AVAILABLE, BUT NOTICE THAT YOU'VE ALREADY EARNED 575 OUT OF 650 POINTS. SO THE POSSIBLE POINTS SHOULD BE 1,000 - 650, SO THERE'S ONLY A POSSIBLE 350 POINTS LEFT IN THE COURSE. SO THE GRADE FOR THE REMAINDER OF THE COURSE MUST EQUAL THE POINTS YOU MUST EARN, 320 DIVIDED BY THE TOTAL POINTS POSSIBLE, REMAINING 350. THIS WOULD GIVE THE GRADE AS A DECIMAL AND THEN TIMES 100 TO CONVERT TO A PERCENTAGE. LET'S GO BACK TO THE CALCULATOR ONE MORE TIME, 320 DIVIDED BY 350, THERE'S THE DECIMAL VALUE x 100. SO IT'S APPROXIMATELY 91.43, WHICH MEANS YOU MUST EARN APPROXIMATELY 91.43% FOR THE REMAINDER OF THIS SEMESTER IN ORDER TO EARN AN "A" IN THE COURSE. OKAY, I HOPE YOU FOUND THIS EXPLANATION HELPFUL.