#26. You are the algebra teacher at the local high school. You assign weights for different types of tests. You must post grades tomorrow, so your assignment tonight is to calculate grades. You must find the weighted mean of the algebra grades. One student made 80 on his first test, 84 on the second test and 90 on the third test. The first two tests counted 40% and the third test counted 20%. What was his final grade?

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Answer 1

To calculate the weighted mean of the student's algebra grades, we will use the weights assigned to each test:

• First Test: 80 (weight = 0.40)
• Second Test: 84 (weight = 0.40)
• Third Test: 90 (weight = 0.20)

The formula for the weighted mean is:

\[ \text{Weighted Mean} = (x_1 \cdot w_1) + (x_2 \cdot w_2) + (x_3 \cdot w_3) \]

where \(x_1\), \(x_2\), and \(x_3\) are the test scores, and \(w_1\), \(w_2\), and \(w_3\) are their corresponding weights.

Plugging in the values:

\[ \text{Weighted Mean} = (80 \cdot 0.40) + (84 \cdot 0.40) + (90 \cdot 0.20) \]

Calculating each term:

• First test: \(80 \cdot 0.40 = 32\)
• Second test: \(84 \cdot 0.40 = 33.6\)
• Third test: \(90 \cdot 0.20 = 18\)

Now, adding these values together:

\[ \text{Weighted Mean} = 32 + 33.6 + 18 = 83.6 \]

Therefore, the final grade for the student is 83.6.