SOLUTION: After taking 4 quizzes, your average is 76 out of 100. What must your average score be on the next five quizzes to increase your average to 81?

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Question 215557: After taking 4 quizzes, your average is 76 out of 100. What must your average score be on the next five quizzes to increase your average to 81?
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
After taking 4 quizzes, your average is 76 out of 100. What must your average score be on the next five quizzes to increase your average to 81?

Step 1. Let x be the average of the next five quizzes.

Step 2. Let 4*76 be the 4 quizzes with each quiz having a score of 76 so the average of the four quizzes is 76.

Step 3. There will be a total of 9 quizzes.

Step 4. The average of nine quizzes is 81=%284%2A76%2B5x%29%2F9. Solve for x as follow

Multiply 9 to both sides of equation to get rid of denominator

81=%284%2A76%2B5x%29%2F9

9%2A81=9%2A%28304%2B5x%29%2F9

729=304%2B5x

Subtract 304 to both sides of equation to get 5x on the right side

729-304=304%2B5x-304

425=5x

Divide by 5 to both sides of equation to solve for x

425%2F5=5x%2F5

x=85

Step 5. ANSWER: To get an overall average of 81, the next five quizzes must average 85.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J