write an inequality an solve

Question

Sam wants to earn at least a B in Math. If he earned the following percents 100, 82 ,70 , 72, 80. What is the minimun grade Sam must earn in order to keep a B average? (Hint: grade b is an 80 an greater  an less than a 90 )

 A: write an solve an algebraic inequality . Show all your work

B:answer the question in the problem an label.

 

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Answer 1

A. b + 5 < 89

b + 5 - 5 < 89 -5 = b < 81    

CHECK YOUR WORK

100 + 82 + 70 + 72 + 80 + 81 = 485

485 / 6 = 80.8 ≈ (approximately) 81%

B. Sam must earn a score of 81% on his next test to earn a B.

 

Answer 2

80 < 100 + 82 + 70 + 72 + 80 + n / 6 < 90

80 < 404 + n / 6 < 90

6 * 80 < 6 * 404 + n / 6 < 6 * 90

480 < 404 + n < 540

480 - 404 < 404 + n - 404 < 540 - 404

76 < n < 136

The minimum score Sam can earn is 76%.

(MATHGEEK)

Comments

A. 80 < 100 + 82 + 70 + 72 + 80 + n < 90
     80 < 100 + 82 + 70 + 72 + 80 + n < 90
                              6
     80 < 404 + n  < 90
                6
     6 * 80 < 6 * 404 + n  < 6 * 90
                             6
     480 < 404 + n < 540
     480 - 404 < 404 + n - 404 < 540 - 404
     76 <         n           <  136
CHECK - minimal - 76%.  100 + 82 + 70 + 72 + 80 + 76 / 6 = 80% (Sam's average).
B. Sam can get a B if he scores between 76, inclusive, and 136 exclusive, on his next test.  So the minimal grade Sam can earn to earn a B in math is 76%.