C or better?

Professor Brown counts her midterm exam as 2/3 of the grade and her final as 1/3 of the grade. Joe scored only 56 on the midterm. What range of scores on the final exam would give Joe a C or better in the course.





90-100=A


80-89=B


70-79=C


60-69=D

C or better?
(2/3)(56) + (1/3)x %26gt;= 70


37 1/3 + 1/3x %26gt;= 70


1/3x %26gt; = 32 2/3


x %26gt;= 98


Joe would have to get a 98 or better on the final to get a C or better in the course.
Reply:Let x be the score on the final to get c or better.


(2/3)(56)+(1/3)x ≥ 70, based on the average score


Multiply by 3,


112 + x ≥ 210


x ≥ 98


It's a big challenge for Joe to get C or better.
Reply:Let x = final grade to get C:





If exactly 70, then:


2/3(56) + 1/3x = 70


37 1/3 + 1/3x = 70


1/3x = 70 - 37 1/3


1/3x = 32 2/3


x = (32 2/3) / (1/3)


x = 98 or higher





Proof:


2/3(56) + 1/3(98) = 70


37 1/3 + 32 2/3 = 70

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