In college algebra a student earns an average grade of 86 on his homework and 75 on his quizzes. What final examination grade will give him a total average of 80 if homework 1/10 , quizzes 3/5 and the final examination 3/10?

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75 average on quizzes
86 average on homework
? on final exam (88)

hw 1/10
quiz 3/5
fe 3/10

80 average total needed

hw 1/10
quiz 6/10
fe 3/10

quiz 60 - 45
hw 10 - 8.6
fe 30 - ? (26.4)

80

8.6 + 45 =
53.6

80 - 53.6

To find the final examination grade that will give the student a total average of 80, we can use the weighted average formula.

Weighted Average = (Weight of Category 1 * Grade in Category 1) + (Weight of Category 2 * Grade in Category 2) + ... + (Weight of Category N * Grade in Category N)

Let's assign variables for the unknowns:
Let the final examination grade be x.

Given:
Homework weight (1/10) = 0.1
Homework grade = 86
Quiz weight (3/5) = 0.6
Quiz grade = 75
Final examination weight (3/10) = 0.3

Since we want the total average to be 80, we can set up the following equation:

80 = (0.1 * 86) + (0.6 * 75) + (0.3 * x)

Now, let's solve the equation for x, the final examination grade:

80 = 8.6 + 45 + 0.3x

80 = 53.6 + 0.3x

Subtract 53.6 from both sides:

26.4 = 0.3x

Divide both sides by 0.3:

x = 26.4 / 0.3

x = 88

Therefore, to achieve a total average of 80, the student needs to score 88 on the final examination.