my name is bla havin and today we're going to work through two examples regarding weighted averages you can see that I've written up here the syllabus for the theoretical class uh let's say the homework worth 10% quizzes 20 uh each exam worth 15% so adding up to 45% and a final which is worth 25% um let's take a student let's say they received a 100% on the homework so our first step is going to be to divide the 100% by 100% to see the total amount they receive receiv on the homework so divided by 100% And that's going to give us one and then what we want to do is multiply that by the weight of each section so for homework that would be 10% 1 * 10% is 10% so the student received a 10% on the homework for quizzes let's say the student received an 89% we are going to again divide that by 100% that's going to give us a decimal of 0.89 and as I said before quizzes are 20% so we multiply 0.89 by 20% this will give us a percentage of [Music] 17.8% and for right now we're going to keep all of our decimal places as it will give us the most accurate answer but at the end we will condense to two sigfigs so let's mark where we will stop uh so for the first exam let's say the student received a 90% uh that will give them a percentage of 13.5% or I'm sorry got ahead of myself 0.90 and we're going to multiply that by 15% which will then give them a percentage of 13.5% next for examp two we'll say 85% this will give them a decimal of 0.85 multiplied by the 15% and this should be a percentage of 12.75% for the last exam we'll say they studied really hard and received a 97% so they will receive 0.97 there uh times the 15% and that should give them a percentage of 14.55% lastly for the final uh the student thinks they're doing really well in the class so they don't study for the final and receive a 70% divide that by 100% 0.70 and we're going to multiply that by the 25% giving the student a 17.5% so the next step is to add all of these up when we do so we get [Music] 85.8% and as I said before we're going to condense this to two sigfigs so this student will receive an 86% in the class so that is the first scenario in this video we're going to work through a different scenario for weighted averages so as you can see we already have calculated uh with the syllabus 15% for the homework 5% for the quizzes uh 15% for the first exam 17 for the second and 18 for the 3D and a 30% Final in this scenario we're going to calculate what we need on the final to receive grades of either a at 93% a B at 85% or a c at 75% so as you saw in the last video video what we did was multiplied what the student received on each section divided that by 100 to get the decimal and multiply that by the weight of each section so as you can see the student received a 90% on the homework giving them a 0.90 * 15% or a 13.5% off for the homework um same for the quizzes they' received 100% on the quizzes so 1 * 5% they received 5% 85% on exam 1 0.85 * 15% 12.75% uh 90% on exam 2 divided 100 0.90 * 177% is 15.3% and a 93% on exam 3 0.93 * 18% was 16.74% this gives a student 6329 of the class now as you can see they've only gone through 70% of the class so if we want to calculate what they have now we'll just divide this by 70% and that'll give you 90% in the class so now what we need to do is calculate what they need on the final and we'll start with the eight to receive a 90% 93% sorry so 63.2 n what we need to do with this is add it to the final what what you could receive on the final but we're going to multiply it by a variable or the grade you receive on the final so plus 30 x and this is all going to be set equal to the 93% or 93 in this case so what we first need to do is subtract 63.2 from from each side and this will give us 30 x = 29.71 um now we just divide by 30 on each side we see that X = 0.99 this means that well we'll multiply this by 100 first the student will need a 99% on the final exam to receive a 93% in the class so now we'll calculate for a b and we said 85% so 85 subtract the 63.2 n and we get 2.71 divide that by 30 and you see the student needs a 0.72 or A 72% in the [Music] class or I'm sorry is 72% on the final to receive an 85% in the class and for the last scenario the student to receive a 75 or in this case of C we'll subtract the 63.2 N that is 11.71 divide by 30 and we see the student only needs 0.39 * 100 a 39% on the final to receive a 75 in the class