Weighted Average Practice Problems & Solutions - Step by Step

Let's solve the problem by applying the steps we outlined:

• Step 1: Identify the grade and weight for each component:
    - Assignment: Grade = 98, Weight = 30% (or 0.30)
    - Exam: Grade = 95, Weight = 70% (or 0.70)
• Step 2: Apply the weighted average formula:
    - Compute the weighted grade for each component:
      Weighted grade for assignment = $98 \times 0.30 = 29.4$
      Weighted grade for exam = $95 \times 0.70 = 66.5$
• Step 3: Sum the weighted grades to find Monica's average grade:
    - Total weighted average = $29.4 + 66.5 = 95.9$

Therefore, Monica's average grade is $95.9$.

To find the weighted average grade, follow these steps:

• Step 1: Convert the percentage weights into decimal form:
• 40% to 0.40
• 20% to 0.20
• 15% to 0.15
• 25% to 0.25
• Step 2: Calculate the contribution of each grade by multiplying it by its weight:
• Grade 68 with weight 0.40: $68 \times 0.40 = 27.2$
• Grade 73 with weight 0.20: $73 \times 0.20 = 14.6$
• Grade 94 with weight 0.15: $94 \times 0.15 = 14.1$
• Grade 91 with weight 0.25: $91 \times 0.25 = 22.75$
• Step 3: Sum the contributions:
$27.2 + 14.6 + 14.1 + 22.75 = 78.65$

Since the weights sum up to 100%, the weighted average grade is directly this sum.

Therefore, the student's weighted average grade is $78.65$.

To solve the weighted average, we will use the following formula:

exam 2 * weight of evaluation 2 + exam 1 * weight of the evaluation 1 = Weighted average

We will place the data in the formula, where the weights will be in decimal numbers:

0.3*79 + 0.7*83 = 
23.7+58.1 = 

81.8

In order to determine the hotel rating, we must calculate an average.

Below is the weighted average formula:

(value A X weight percentage A)+(value B X weight percentage B)...

First, let's add up all the percentages:

$50\%+30\%+10\%+10\%=100\%$

Now we must multiply each factor by its weight percentage, convert the percentages to decimal numbers, and add them as follows:

$4.5\times0.5+4\times0.3+5\times0.1+3\times0.1=$

We then proceed to solve the multiplication exercises:

$2.25+1.2+0.5+0.3=$

Finally we add them up and obtain the following: 4.25 which is the hotel's overall rating.

To calculate Gabriel's final weighted average, we'll use the formula for a weighted average:

$\text{Weighted Average} = (\text{Test 1 Grade} \times \text{Weight 1}) + (\text{Exam Grade} \times \text{Weight 2}) + (\text{Test 2 Grade} \times \text{Weight 3}) + (\text{Project Grade} \times \text{Weight 4})$

Next, calculate the contribution of each component:

• Test 1 Contribution: $84 \times 0.30 = 25.2$
• Exam Contribution: $73 \times 0.15 = 10.95$
• Test 2 Contribution: $87 \times 0.35 = 30.45$
• Project Contribution: $92 \times 0.20 = 18.4$

Now, add all these contributions to find the final weighted average:

$\text{Weighted Average} = 25.2 + 10.95 + 30.45 + 18.4 = 85$

Therefore, Gabriel's final weighted average is $\boxed{85}$.