Worksheet titled "Weighted Averages Worksheet" featuring four problems related to calculating weighted averages in academic and competitive scenarios.

Let’s solve each problem step by step. We’ll calculate weighted averages carefully, checking our math as we go.

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Problem 1:

We are told the weights:
- Quizzes (Q1–Q5): 15% total → so each quiz is 15% ÷ 5 = 3% each
- Exam 1: 20%
- Exam 2: 20%
- Homework (HW1–HW4): 20% total → each HW is 20% ÷ 4 = 5% each
- Final: 25%

Student X’s scores and possible points:

| Category | Score | Possible | % of Grade | Points Earned / Total | Weighted Contribution |
|----------|-------|----------|------------|------------------------|------------------------|
| Q1 | 5 | 9 | 3% | 5/9 ≈ 0.5556 | 0.5556 × 3 = 1.6667 |
| Q2 | 6 | 9 | 3% | 6/9 = 0.6667 | 0.6667 × 3 = 2.0000 |
| Q3 | 8 | 9 | 3% | 8/9 ≈ 0.8889 | 0.8889 × 3 = 2.6667 |
| Q4 | 8 | 9 | 3% | 8/9 ≈ 0.8889 | 0.8889 × 3 = 2.6667 |
| Q5 | 9 | 9 | 3% | 9/9 = 1.0 | 1.0 × 3 = 3.0000 |
| HW1 | 10 | 10 | 5% | 10/10 = 1.0 | 1.0 × 5 = 5.0000 |
| HW2 | 10 | 10 | 5% | 10/10 = 1.0 | 1.0 × 5 = 5.0000 |
| HW3 | 0 | 10 | 5% | 0/10 = 0.0 | 0.0 × 5 = 0.0000 |
| HW4 | 8 | 10 | 5% | 8/10 = 0.8 | 0.8 × 5 = 4.0000 |
| EX1 | 41 | 53 | 20% | 41/53 ≈ 0.7736 | 0.7736 × 20 = 15.4717 |
| EX2 | 48 | 56 | 20% | 48/56 ≈ 0.8571 | 0.8571 × 20 = 17.1429 |
| FINAL | 89 | 92 | 25% | 89/92 ≈ 0.9674 | 0.9674 × 25 = 24.1848 |

Now add up all weighted contributions:

Quizzes: 1.6667 + 2.0000 + 2.6667 + 2.6667 + 3.0000 = 12.0001
Homework: 5.0000 + 5.0000 + 0.0000 + 4.0000 = 14.0000
Exams: 15.4717 + 17.1429 = 32.6146
Final: 24.1848

Total grade = 12.0001 + 14.0000 + 32.6146 + 24.1848 = 82.7995 → approximately 82.8%

✔ So for part (a), student X’s grade is 82.8%

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Part (b): Drop the missed homework assignment (HW3, which was 0/10).

That means we remove HW3 from calculation. But now, homework is only 3 assignments instead of 4. The original weight for homework was 20% total — if we drop one, do we redistribute? The problem says “drop the homework assignment he/she missed” — it doesn’t say to reweight, but in most grading systems, if you drop an assignment, the remaining ones make up the full category weight.

So let’s assume: Homework is still 20% of grade, but now based on 3 assignments (HW1, HW2, HW4). Each would be 20% ÷ 3 ≈ 6.6667% each.

Recalculate homework contribution:

HW1: 10/10 = 1.0 → 1.0 × 6.6667 = 6.6667
HW2: 10/10 = 1.0 → 1.0 × 6.6667 = 6.6667
HW4: 8/10 = 0.8 → 0.8 × 6.6667 = 5.3334

New homework total = 6.6667 + 6.6667 + 5.3334 = 18.6668

Everything else stays the same:

Quizzes: 12.0001
Exams: 32.6146
Final: 24.1848

New total = 12.0001 + 18.6668 + 32.6146 + 24.1848 = 87.4663 → approximately 87.5%

✔ So for part (b), dropping HW3 gives student X a grade of 87.5%

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Problem 2:

Weights:
- Quizzes: 20% total → 3 quizzes given, so each quiz is 20% ÷ 3 ≈ 6.6667%
- Homework: 20% total → 3 assignments given, so each is 20% ÷ 3 ≈ 6.6667%
- Exam 1: 15%
- Exam 2: 15%
- Final: 30%

You have:
- Quiz scores: 6/9, 8/10, 9/9
- Homework: 9/11, 10/10, 4.5/7
- Exam 1: 58/63

Calculate each component:

Quizzes:
Q1: 6/9 = 0.6667 → 0.6667 × 6.6667 ≈ 4.4445
Q2: 8/10 = 0.8 → 0.8 × 6.6667 ≈ 5.3334
Q3: 9/9 = 1.0 → 1.0 × 6.6667 = 6.6667
Quiz total = 4.4445 + 5.3334 + 6.6667 = 16.4446

Homework:
HW1: 9/11 ≈ 0.8182 → 0.8182 × 6.6667 ≈ 5.4547
HW2: 10/10 = 1.0 → 1.0 × 6.6667 = 6.6667
HW3: 4.5/7 ≈ 0.6429 → 0.6429 × 6.6667 ≈ 4.2860
Homework total = 5.4547 + 6.6667 + 4.2860 = 16.4074

Exam 1:
58/63 ≈ 0.9206 → 0.9206 × 15 = 13.8095

Exam 2 and Final: Not taken yet → contribute 0 for now.

Current grade = Quiz + Homework + Exam1 = 16.4446 + 16.4074 + 13.8095 = 46.6615

But wait — this is out of what total percentage? We’ve only done parts that add up to:

Quizzes (20%) + Homework (20%) + Exam1 (15%) = 55% of the course.

So your current score is 46.6615 out of 55% possible so far.

To find your current grade *as if the course ended now*, we can compute:

(Your earned points) / (Total possible points so far) × 100

But actually, since weights are fixed, and you haven’t taken Exam2 or Final, your current grade is just the sum of the weighted components you’ve completed — which is 46.66%. However, that’s not how grades usually work — typically, your current grade is calculated as (points earned so far) / (total points possible so far), then scaled to 100%.

Let me clarify: In many classes, your "current grade" is computed by taking all graded work so far, adding up your percentage in each category, multiplying by their weight, and summing — even if some categories aren't complete. That’s what we did above: 46.66%.

But sometimes, teachers normalize it to 100% based on what’s been assigned. Let’s check both ways.

Actually, looking at the question: “What is your current grade in the course?” — since Exam2 and Final haven’t happened, they don’t count yet. So your grade should be based only on what’s been graded.

In standard practice, we take the weighted average of what’s been completed. Since quizzes, homework, and exam1 are done, and they total 55% of the course, your current grade is the sum of those weighted scores: 46.66%

But that seems low — let’s double-check calculations.

Alternative approach: Compute overall percentage based on points earned vs points possible so far.

Total points possible so far:

Quizzes: 9+10+9 = 28
Homework: 11+10+7 = 28
Exam1: 63
Total possible = 28 + 28 + 63 = 119

Points earned:

Quizzes: 6+8+9 = 23
Homework: 9+10+4.5 = 23.5
Exam1: 58
Total earned = 23 + 23.5 + 58 = 104.5

Current grade = (104.5 / 119) × 100 ≈ 87.815%

Ah! This makes more sense. The first method assumed each category is fully weighted even though not all items are done — but in reality, for current grade, we often use raw points earned over points possible so far.

The problem says: “you just found out that you scored a 58/63 on the first exam... received a 6/9, 8/10, and 9/9 on the first three quizzes as well as a 9/11, 10/10, and 4.5/7 on the first three homework assignments.”

It doesn’t say there are more quizzes or homework — it says “first three”, implying these are all for now. And since it’s week 5, probably no more until later.

But the weights are given for the whole course. So to compute current grade, we should use the weighted average of what’s been completed, assuming the rest will be zero for now? Or scale to 100%?

I think the intended interpretation is: calculate the weighted average using the scores you have, with the given weights, and ignore the uncompleted parts (i.e., treat them as 0 for now). But that would give a very low grade.

Looking back at Problem 1, they didn’t drop anything unless specified — here, for current grade, we include only what’s been graded, with their full weights? That doesn’t make sense because exams 2 and final are big chunks.

Standard academic practice: Your current grade is the weighted average of all graded components, with ungraded components not included (or treated as 0, but that penalizes you). Actually, most systems calculate current grade as (sum of weighted scores for completed work) divided by (sum of weights for completed work), then multiplied by 100 to get a percentage.

Let me try that.

Completed work weights: Quizzes 20% + Homework 20% + Exam1 15% = 55%

Weighted scores earned: as before, 16.4446 (quizzes) + 16.4074 (homework) + 13.8095 (exam1) = 46.6615

Then current grade = (46.6615 / 55) × 100 ≈ 84.84%

This is reasonable.

Some might argue to use raw points: 104.5 / 119 ≈ 87.82%, but that ignores the different weights — for example, exam1 is worth more than a quiz, but in raw points, exam1 has more points, so it's somewhat accounted for.

But the problem specifies weights, so we should use weighted average.

Let me recalculate the weighted scores more accurately.

Quizzes:
Q1: 6/9 = 2/3 ≈ 0.6666667 × (20/3)% = 0.6666667 × 6.6666667 = 4.444444
Q2: 8/10 = 0.8 × 6.6666667 = 5.333333
Q3: 9/9 = 1 × 6.6666667 = 6.666667
Sum quizzes = 4.444444 + 5.333333 + 6.666667 = 16.444444

Homework:
HW1: 9/11 ≈ 0.8181818 × 6.6666667 ≈ 5.454545
HW2: 10/10 = 1 × 6.6666667 = 6.666667
HW3: 4.5/7 ≈ 0.6428571 × 6.6666667 ≈ 4.285714
Sum homework = 5.454545 + 6.666667 + 4.285714 = 16.406926

Exam1: 58/63 ≈ 0.9206349 × 15 = 13.809524

Total weighted score = 16.444444 + 16.406926 + 13.809524 = 46.660894

Total weight used = 20 + 20 + 15 = 55%

Current grade = (46.660894 / 55) × 100 = ?

46.660894 ÷ 55 = 0.8483799

×100 = 84.84%

Yes.

If the teacher uses raw points without weighting, it would be different, but since weights are given, we use weighted average normalized to completed work.

So current grade is 84.8%

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Problem 3:

Categories: taste, presentation, addressing challenge — each worth 18 points max.

Weights for final score:
- Taste: 60%
- Presentation: 25%
- Addressing challenge: 15%

Largest possible score: if someone gets 18 in each category.

Weighted score = (18/18)*60 + (18/18)*25 + (18/18)*15 = 60 + 25 + 15 = 100

So largest possible score is 100.

Now Mary:
- Taste: 15/18
- Presentation: 9/18
- Challenge: 14/18

Mary’s score = (15/18)*60 + (9/18)*25 + (14/18)*15

Calculate each:
15/18 = 5/6 ≈ 0.8333 → 0.8333*60 = 50
9/18 = 0.5 → 0.5*25 = 12.5
14/18 ≈ 0.7778 → 0.7778*15 ≈ 11.6667

Total = 50 + 12.5 + 11.6667 = 74.1667

John:
- Taste: 18/18 = 1 → 1*60 = 60
- Presentation: 7/18 ≈ 0.3889 → 0.3889*25 ≈ 9.7222
- Challenge: 13/18 ≈ 0.7222 → 0.7222*15 ≈ 10.8333

Total = 60 + 9.7222 + 10.8333 = 80.5555

John has higher score: 80.56 > 74.17, so John wins.

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Problem 4:

Competition: 3 dishes.

First two dishes: each graded on taste (60%), presentation (25%), creativity (15%) — each category max 20 points.

Third dish: taste (70%), presentation (30%) — each max 20 points.

Weights for final score:
- Dish 1: 30%
- Dish 2: 30%
- Dish 3: 40%

Jim’s scores:

Round 1 (Dish 1):
Taste: 17/20
Presentation: 18/20
Creativity: 19/20

Weighted for dish 1: (17/20)*60 + (18/20)*25 + (19/20)*15
= (0.85)*60 + (0.9)*25 + (0.95)*15
= 51 + 22.5 + 14.25 = 87.75

Since dish 1 is 30% of final, contribution = 87.75 * 0.3 = 26.325

Round 2 (Dish 2):
Taste: 18/20
Presentation: 18/20
Creativity: 16/20

Weighted: (18/20)*60 + (18/20)*25 + (16/20)*15
= 0.9*60 + 0.9*25 + 0.8*15
= 54 + 22.5 + 12 = 88.5

Contribution to final: 88.5 * 0.3 = 26.55

Round 3 (Dish 3):
Taste: 15/20
Presentation: 18/20
(no creativity)

Weighted: (15/20)*70 + (18/20)*30
= 0.75*70 + 0.9*30
= 52.5 + 27 = 79.5

Contribution: 79.5 * 0.4 = 31.8

Jim’s total = 26.325 + 26.55 + 31.8 = 84.675

Pam’s scores:

Round 1:
Taste: 17/20
Presentation: 15/20
Creativity: 18/20

Weighted: (17/20)*60 + (15/20)*25 + (18/20)*15
= 0.85*60 + 0.75*25 + 0.9*15
= 51 + 18.75 + 13.5 = 83.25

Contribution: 83.25 * 0.3 = 24.975

Round 2:
Taste: 16/20
Presentation: 16/20
Creativity: 18/20

Weighted: (16/20)*60 + (16/20)*25 + (18/20)*15
= 0.8*60 + 0.8*25 + 0.9*15
= 48 + 20 + 13.5 = 81.5

Contribution: 81.5 * 0.3 = 24.45

Round 3:
Taste: 19/20
Presentation: 19/20

Weighted: (19/20)*70 + (19/20)*30
= 0.95*70 + 0.95*30
= 66.5 + 28.5 = 95

Contribution: 95 * 0.4 = 38

Pam’s total = 24.975 + 24.45 + 38 = 87.425

Compare: Jim 84.675, Pam 87.425 → Pam wins.

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Now, compiling all answers:

Problem 1a: 82.8%
Problem 1b: 87.5%
Problem 2: 84.8%
Problem 3a: 100
Problem 3b: John wins
Problem 4: Pam wins

Let me write them clearly.

Final Answer:
1a. 82.8%
1b. 87.5%
2. 84.8%
3a. 100
3b. John
4. Pam